All you need for a wedding is two people to get married, someone to perform the service,. a wedding license, a witness or two (if you even need them, CT doesn't require a witness at all!) if you want guests as well, a reception can be as simple as a sheet cake and some fruit punch in a space large enough to accommodate the number of guests.
My family did help pay for the wedding. It cost us $6k. My husband and I paid $2k of it. We had our wedding at a spa that my company owns (I got an employee discount), we had the dinner there as well. We opted for no dancing since we both have two left feet. We did minimal decorating since the space was already beautiful to look at. I did get a wedding dress, he wore a tux. We had a matron of honor, a best man, one groomsman and a flower boy. There were 23 people there including the wedding party. Everyone that was there was impressed even though it was a small wedding.
Had it been done the way that my husband was suggesting, we would have been married on the beach by a justice of the peace with just our immediate family there. We probably would have gone out to dinner afterwards to celebrate. We were married in mid-April. I have a friend that would have done the photography if I had asked as a gift.
As a PP said, decide what it is that the TWO OF YOU WANT. Prioritize what's important. The nice thing about paying for it yourselves is that no one else gets a say in what you plan. :) My husband wanted a justice of the peace. I wanted a wedding dress and nice dinner. I wanted very few guests so that I didn't get nervous. It all worked out in the end.
Good luck and have fun! The end result will be spending the rest of your life with your partner in crime. :)