For a first birthday, the celebration is undoubtedly mostly for the parents and friends and relatives. I was lucky enough to be able to take ds the 800 miles "back home" so he could have his celebration with his only cousins. They're older than him, but I thought that's the way it should be - just family, low key. All of our playgroup friends had parties that year and we went to some and just gave gifts for others. I was a little disturbed that the trend seemed to be if you hosted a party you got a gift. We weren't in need of gifts, but I was a little offended that these were our "friends" and they didn't think of us because we didn't host a party they could attend.
Anyway, that was a little off track from your question. I wouldn't deny your friends and family the chance to shop for a little one. . . it's fun. If any of them, for whatever reason, should think YOU are soliciting gifts, they'll probably spend minimally anyway, so don't worry about them. If you get things that you don't need, exchange them for something you want. Even if you're set for life on hand-me-downs, something new every now and then is always good. If anyone contacts you beforehand and asks for gift suggestions, I don't see anything wrong with telling them he doesn't need anything so whatever they would like for him to have would be fine, or having a list of some things you think he might like. I do agree with the idea that including a "no gifts. . " statement is presumptive and in bad taste.
We just had ds's 2nd year party today and he enjoyed the kids, even though it might be a good idea to stick to the rule of thumb one guest per year of age of child. I probably invited too many, but being the cold and flu season, I expected some cancellations and I couldn't choose who to exclude! We ended up with 4 kids, their mommies, and a baby sister and they all seemed to have fun (except for the biting incident which I'm going to post about on another board). DS loved unwrapping his gifts and was a very gracious host. I think that it's a good experience at this age for the kids to choose gifts to give their friends and for the recipient child to learn how to be a grateful receiver. Not to mention all the decision making ds got to do in choosing party decorations, cake, favors, etc. During the planning process, I was disheartened that ds would start whining when we discussed the prospect of sharing his cool toys with his friends at the party. He would communicate that only HE could play with them. But, in the end, he came through admirably for his age. He actually had fun watching the other kids play with his toys. . . except when they took his train track apart. Overall he had a blast and enjoyed all the "trappings" - cake, snacks, games, and gift opening.
Whatever you do, have fun. And designate a photographer! You'll be too busy.