I tend to agree with the other person who wrote that food and chairs should be provided by you
you know your wedding guests better than we. Some families are so helpful and family oriented that they will bend over backwards to be accomodating to a couple on a thin budget. If you believe that both of your families are that relaxed and helpful, I'd say go for it on your invitations. Paint the picture of a very relaxed and infomal event where a variety of chairs and people sitting wherever they put their chair down will be OK with you. Offer to provide a chair for those that do not have one or for the elderly who it might be an inconvenience to try to get one there.
All of your wedding decisions should be made with your needs AND the needs of your guests in mind.
In my humble opinion a wedding reception is an opportunity for you to thank the people in your life that have help to bring you to this important day, having them share in your day and provide them with a meal as a thank you. Why not have a ceremony and dessert? or Perhaps you could limit the guest list to fit your budget. I really do not think that it is appropriate to ask a guest to bring their own seating and food. Two years ago I hosted my brothers wedding, we asked 5 close family members to share in the cooking, set up and clean up. It was a wonderful wedding, most guest thought we had hired a caterer.
That is part of my plan to go to the dollar store and get the table clothes in our colors. As well as a small table with the guest books that I have made up. And a few bigger tables to put the favors on.
There is nothing wrong with having a casual celebration after your wedding ceremony, but I would probably leave detail instructions such as potluck and chairs to word of mouth, email, notes, etc. and leave it off the invitation.
Rev. Ann Fuller