As far as the actual swapping, we always did it like this.
Round one - each person go pick up one plant.
Round two - each person go pick up two plants.
Round three - three plants each, etc...
When what you brought is gone, you stop picking plants. When everyone is finished, any leftovers are put up for grabs. Usually the people who didn't have much to bring end up with these, which is cool. We always asked people to bring other gardening items if they wanted to, which were usually a "great find" to someone else. Like bundles of pots, stakes, tags, baskets, bird feeders. Whatever you bought but ended up not wanting or using. You can choose to swap items separately, or as part of the overall swap included with plants. Just as long as everyone understands what is going on, however you want to do it should be fine.
Covered shelters at parks are great places for a swap. Usually you can reserve them for a nominal fee, you have the cover and picnic tables, and usually a restroom facility, trash cans, and hopefully a playground for the kids. You can split the cost evenly, like if it costs $40 and 30 people show up, everyone chips in $1.35. I would include the cost of cups, plates, etc, bought for the event, or solicit donation of those items beforehand, which is a lot easier especially if there is a meal but not everyone participates in that part. We would usually do the meal first so everyone gets a good opportunity to chat about their plants before swapping.
Agree, the hostess should solicit cleanup help beforehand, or at least remind everyone to take all of their stuff home and throw away all of their trash if at a park.
If you're unsure about shade at the swap location and you have all shade-lovers, a folding table could be needed to put the plants UNDER!
