I think the variety you've got with the food is fine (as long as you have no vegetarians on your guest list), but I agree that the quantity you've set up is almost certainly not going to be enough for 20 people unless your party is very short. I also agree that the quantity is fine to start with, but you're going to need to be prepared (and probably plan) to order more as the party goes on.
I like Margo's suggestion of talking with the servers ahead of time to discuss a limit on beer, and having them check with you when you hit it so you can reevaluate if you need to. I think you should probably also do that for the food. If your party is, say, 2 hours, you could have the servers automatically replenish the food until an hour has passed or you've hit a predetermined limit (whichever comes first). The limit for both the drinks and the food can either be a set dollar amount (keep it coming until my bill is $100) or a set number of orders. Once the limit or the time has been reached, have the servers check with you.
Another way you could handle it is to just monitor the food people are eating and make new orders of things yourself as you see that they are low. However, that would make it harder for you to keep track of what you are spending, and it will make it harder for you to enjoy the party itself. I'd go with establishing a set limit and having the servers alert you if the bar is willing to do that, just because it will probably enjoy yourself more that way. If they aren't, and you have to keep track of things yourself, I'd advise figuring out how many of each item you're willing to order without thinking about it (and write that number down), and then mark each order off on a piece of paper so you don't have to do a bunch of mental arithmetic while you're trying to enjoy yourself.
For budgeting purposes, I would probably talk to the bar and see if they can give you an idea of what a group that size would normally consume. That should allow you to get an idea of the total cost, although it would be prudent to be prepared to spend more than that (you just have to decide how much more). If you have a realistic but generous budget in mind, you will hopefully not get an unpleasant surprise when you go to pay your bill at the end of the party.
In terms of hosting, I think that what you are planning sounds lovely. If you are okay with guests ordering their own drinks/food during your party, then I would just say, "X, Y, and Z are on us for the next two hours -- if you want anything else, you'll need to order it from the bar/have the server set up a tab for you."
If, on the other hand, you'd really prefer that people not order other food/drink during the party time, I would say, "We're providing the food and drink for the next two hours, so please, help yourselves to it!" In that scenario, I'd make sure the bar doesn't give menus to the guests, and that you have ordered everything in advance.