Oh, you have to have a first birthday party for that little sweet one! I had one for my son and I invited friends that I had had forever, friends from work, family, and my best friend who had kept him for 4 1/2 months when I went back to work so I didn't have to put him right into daycare at 8 weeks old. You can invite whoever you want. I did put on the invitations that gifts were not necessary, that their presence to celebrate the first wonderful year of many was all that was required.
It will really depend on what time that you are doing the party as to what kind of food that you should have. If you do it in the afternoon, you could just do some 'finger' type foods since they would have already had lunch. That is unless you want to do a meal. I had enough to do, so I did a 3 o'clock party and had things like nuts, chex mix, party platter to make small sandwiches, etc. And of course, you have to have a cake for the guests and one for little bit!!! That was the best part for me was to watch him try to figure out what exactly the cake was and then tear into it!
It is definitely a day to remember, so enjoy it, take lots of pictures and enjoy putting them in an album to relive it forever. You will be glad that you did.
Good luck and let us know how it goes!