I have 3 experiences with a 1st birthday- 3 SIL's, 4 boys (1 set of twins). The first one did a similar theme- at the park, with a bbq and chips and dip, but there were a large number of kids- only because alot of their friends have little ones, so they were welcome to bring them. The kids ran around the park, went down the slides, etc. It was a family affair. The only things that were specifically for the baby were a pinata (he was a walker early on) and the cake, which was done with a cool whip frosting so it had less sugar. The 2nd sister did a smaller family venue at her home and there were only 2 other kids there. We had burgers and salad and sides, the kids had a kiddie pool to swim in, and then we had cake. He opened presents (mommy opened most of them) and mashed cake crumbs all over the floor (put a sheet under the kid, you'll thank yourself later for only haveing to wash the one thing).
The 3rd sister, because her kids were also being dedicated by a local minister, had a huge party. The boys had their dedication between morning nap and lunch. Then there was afternoon nap while we set things up in the backyard. Now, this sister is also much more socially a butterfly, so there were LOADS of people there. Plus her husband is a professor, so they know a lot more people. ALl of these people came, with their kids. We had a bbq, ate, lounged, watched sports, and the boys ran around the backyard with their toys until it was time for bed. The one thing I will say is that some guests over stay their welcome and were there until after 10:30. The boys went to bed at 7:30. I am not saying all people are like that, but some just don't know when to go home, so you may need to prod them along. But the party for a 1 year old (great theme by the way) is about the family and friends seeing the baby and enjoying your family's company. They bring a few presents, let the kids run around and play, and have cake. When they get older and can remember more of their birthdays (take lots of pictures of this first one, too), then go all out with more games and details.
Good luck and have fun!
-E. M