With this additional information ... I've done on two occasions something similar (out of my pocket) what you are doing now.
From your second statement, it appears that you're doing this up front. This is a good idea to develop the "team mentality". In this case, I think what you're looking for is something for a team-identification. The trick is to avoid tchotchkes and to try to come up with something that is appropriate at the corporate, project and "usefulness" level as well as doing the "team building" thing. I was with a consulting organization where we once set up a laser-tag day. We got permission for everyone to take the afternoon off and we had it set up for matches between management and everyone else; the consultants and the company; a free-for-all. About a week before we did it, the project was cancelled.
From your fourth statement, it seems that this is coming at the end. In this case, you are already a team and the objective is to commemorate the success (and even the worst project has some successes) of the endeavour. In this case, I'd do the dinner. Since it's on your tab, you pick up the cost of the food and the individuals pay for their drinks.
As an alternative (I'm not sure where you are so it could be summer or winter!) you might want to consider a catered barbeque. You could do it at your place, or in a local park (attendees could bring their families) or at the boss's house (it would be a good idea to clear it with him first!). The advantage of the park is that it will almost certainly be non-alcoholic -- the disadvantage is that you'll need to arrange for permits and you'll also want to think about a rain date. The advantage of the boss's house is that it's his back yard that needs to be set up (not yours!) -- the disadvantage is that alcohol will probably be present.
If you are doing the catered barbeque, try to move up from simple burgers and hot dogs -- perhaps something like meat skewers (different meats and different sauces). You can also do veggie/fruit skewers for vegetarians.
Thank you, too, for your kind words.