Matushka Ann Lardas
I've seen a wide range of options, ranging from: Trapeza  as a Given, the Agape potluck, for which there is no charge and everyone brings what they can every week. This can lead to interesting meals, but I think it's the best model, as it brings people together and everyone knows every week what is expected of them.
Trapeza as an Agape meal served in teams, like the Dallas model where there are three teams that take turns providing trapeza each week at no cost. Because the teams rotate, people wind up cooking or buying something to bring maybe every three weeks or so. This makes for less stress on parishioners, as you only have to do something once every three weeks, and it is still close to the original Agape meal model. Good for parishes where not everyone can come every Sunday!
Trapeza as Parish Outreach with sporadic fund raising, like in Wilkes-Barre where they have teams that provide coffee and something light three times a month, while once a month they have a fund raising dinner for which there is a charge. This allows the parish to raise money and gives everyone fair warning when a fundraiser is coming up, and allows for easy fellowship the rest of the time. Someone pointed out to me that when you step into a Russian parish, you're asked for money at the candle counter, at the collection, after kissing the cross, and again at trapeza. This can be a turn-off. By using trapeza more as a time to be together and less as a fundraiser, this feeling is mitigated. And still, they do get to raise money for church projects, which is one of the functions of the Sisterhood, though not the only or even the most important. (The charter calls for such things as visiting the sick, providing for a church school, encouraging those who were married outside the Church to be properly married by the Church, etc.)
Trapeza as a Fund Raiser as well as outreach, the Boston Holy Epiphany Church model where people take turns making trapeza for which there is always a set charge, the funds going generally for important goals like frescoing the church. Because everyone knows how much it will cost every week, they can calculate the expense, and someone generally offers to treat guests. I believe there's also a less expensive "coffee and cake" option. By working in teams of two or three families, women share the expense and the work, and often get to know each other better for spending time in planning, cooking, and cleaning up.
Trapeza as an agape meal with the "bachelor option," which we did at St Vladimir's in Houston, where various people would bring what they could every week, without charge but with a basket for voluntary contributions, so those who cannot cook or who want to contribute financially could put what they liked in the basket. People who couldn't cook had been reluctant to stay. Putting out a basket made those who couldn't cook (students, the elderly) feel that they could participate without "being a drain," and provided funds for paper plates, plastic silverware, etc. In fact, the contributions also covered items like Communion wine.
The "à la carte" option which I hear they use at Synod, where it's a dollar for coffee, a dollar for cake, a dollar for a sandwich, and people buy what they like and can afford, proceeds going to the Sisterhood for important projects. This allows those with not so much income to stay, and meet others, and talk, and still the Sisterhood has an income for projects. Then there's the Three Families Do Everything option, which many parishes fall into and are lurched out of. It happens, the people who do everything get fed up, everyone goes hungry for a week or two, and things change for the better. This is a situation to watch out for, because no matter what model you use, you can fall into this.
Generally mission parishes go for the rotating team option, often the best choice if you have people who live far away and cannot come every week. Whatever you do, assign someone (generally the Senior Sister, sometimes by default the matushka) to coordinate efforts if you don't use teams, otherwise you might wind up with five kinds of potato salad and nothing else (as we did once). It's easier if two or three families work together.
In Boston, where two or three women sign up together, generally one will bring the soup and bread, the other the main dish and salad, another will do dessert and coffee. But it's important to emphasize that everyone can contribute. Years back, our warden spoke on the subject after trapeza one week. The next Sunday I was sick and was staying home from church. Our James, then five, came back into the house after Father George had marshalled the kids into the car, and grabbed the container of fasting cookies I'd bought at the Hong Kong Market for him earlier in the week. "Mom," he said solemnly, "I'm bwinging this for twapeza." "Okay, you may, but, why?" I asked. "Uncle Rusty said last week, Mom, that EVEN the unmarried young men in the parish should bring something for twapeza. And Mom!" he said gravely, "I'm not married!" There is no arguing with some logic.
It's good to encourage kids to contribute. I was tired last Saturday so our Nicholas, 11, volunteered to cook. He made cakes for trapeza, following the directions on the back of the box with very little help from me. I had purchased frosting, but dying it blue was his idea, and was a nice touch. Xenia has often made St. Phanourios cake for trapeza when her binder or school books or other important things turned up after being missing. At eight, James can follow the directions for heating something in the microwave; it's a start. And when I was a teenager, the Church School in Boston made the meal one Sunday during Lent and sent the money to the orphanage in Chile. Children who are too young to cook can help set, clear and wipe tables. Johnny, now four, loves to fold chairs. They're a little taller than he, when folded, and he gets this feeling of accomplishment, plus people praise him for helping. If someone seems shy about participating, I find if helpful to hand him a dish and say, "Can you put this on the counter for me, please?" Guys get into the swing of things if you hand them something and tell them what you want done with it. ("Would you mind slicing this loaf of bread?" "Help me put these things on plates while we talk!") It took me years to figure this out, so I pass it along gratis to save you time.
You have to consider your people's needs and how far they travel, also. For five years we had no a.c. in our car. That limited our choices for food to bring (no baked Alaska! And if we're prudent, no shrimp, either, nor mayonnaise in August). If you have people coming from far away, coffee and cookies may be all they can do, but if you team a family that travels with a family who doesn't travel as far, that helps. People who travel long distances might be comfortable bringing soda, bread, packaged cookies, that sort of thing. I've learned, after we turned right and the beans spilled all over the trunk, to put food that could leave its container into a big Rubbermaid bin. Also, I like to make cakes that don't require frosting, as it's that much less potential for disaster, and if I make soup, I don't count on all of it making it to church still in the pot. That's just a given, and accepting it makes life easier. To limit the scope of damage, I cover the pot with plastic wrap and make sure to put the pot on a dead towel (for padding, insulation, and absorption) in the bin. Also, if you put plastic wrap over containers with lids, and then place paper towels between the container and lid, the lid doesn't bang and chip as you drive.
You won't have to worry about glass shards in the food, and your dishes will last longer. At St. Vladimir's in Houston we had neither a stove nor, for the longest time, hot water, so I brought everything already cooked and just placed it on a warming tray, heated dish water in the coffee maker for dishes going home with other people and just washed ours when we got home. I've come to see the value in bringing everything already cooked. You don't have to miss church to prepare food when you cannot even taste to see if you've seasoned it properly. If you make the main dish and dessert before leaving for Vigil and refrigerate it overnight, you can pick up bagged salad and a loaf or two of french bread at the grocery store and have a full meal ready to eat without missing any more of the service than it takes to turn on a warming tray or pop something into the microwave. Some people find a rice cooker an enormous help, as you put the stuff in before church and when you come out, it's cooked. I feel the same way about my crockpot, but I make sure to cook the food first and let is just heat at church, after the time that the ingredients were still crunchy when it was time to eat.
Everyone should help with clean-up, but sometimes people can't stay. Those people should be tapped for help with setting up, so if anyone complains you can say, "But they set up all the tables!" Make sure that you don't wind up with the same few families doing all the clean-up all the time, or burnout sets in. Cooking and cleaning together can bring people together, and offer an opportunity to talk. There's something relaxing about having your hands in warm soapy water and turning a big mess into a gleaming collection of dishes and pans. It makes for easier conversation. Sometimes people are reluctant to ask others to help. This is where a priest or matushka (or especially a babushka) can be most helpful. If someone's just standing there, hand him a broom or a dish rag and tell them what needs doing. (This works best if you are wielding a dishtowel or sponge yourself!) Hearty engagement beats simmering resentment any day. Just as children are secretly happier when they have chores, if you get people to help, briefly, with set-up and clean-up for meals, they will be happy to be a part of things, and, except for dishwashing, very few clean up tasks really take more than five minutes.
Every system has its upside and downside. Find out what works for your parish, and don't be afraid to stop doing something that doesn't work. Often it's a relief if the priest announces that something isn't working out and that a new solution is needed. Most people are humble, at heart, and don't want to speak up and say such things, even if they think them. Chances are that if something is too much of a burden for you, it's too much for others, also, and you need to readjust things. Be understanding of limitations, and willing to be flexible.
Hope this helps!
 In Russian, a meal. In English-language Orthodox circles it has specifically come to mean a meal after a church service, usually in the church hall.