Vail can be tough on a tight budget. You are correct that mistakes can cost you. On the mountain options are varied, but all are pricey. Mid-Vail and Eagles nest are pretty typical cafeteria style eateries. Two Elks lodge offers a few more options like stir fry, burrito/wraps and salad bar as well as the typical burgers, fries, soups, chili options. A basic burger fries and a drink is going to run you $15-$20. Nothing like a $5 Gatorade. There are full service groceries in Vail, or if you are driving up from Denver, Silverthorne has plenty of shopping options. If you are looking to limit the cost on the mountain (lift tickets are expensive enough), it's pretty easy to pack beef jerky, fruit, sandwiches, nuts, etc. and there is plenty of free water in the on mountain dining establishments. There is a Costco about 30 minutes west of Vail in Gypsum, and a couple in the Denver area readily accessible from the expressway. Great for stocking up on cliff bars, jerky, nuts, trail mix, etc.
In terms of restaurants the ones mentioned are fine. Most of the stuff in the village is premium priced. I have eaten at a bunch of them and while I can't say I have had a horrible meal at any, most are more expensive than you would expect for a similar meal elsewhere. Sweet Basil, Pepi's, Montauk, as mentioned Russells has pretty good steak, ribs, chicken, etc. Elways and Vail Chop House serve similar fare, they are about what you would expect from a steakhouse, with everything being about 20% more because you are in Vail. If you compare the prices between Elways in Denver to in Vail you can see the markup. There is a good and reasonably cheap Ramen place right next to the Safeway in West Vail, called Nudoru.
If you don't mind driving, you can go in either direction. East of Vail 20-30 minutes in Dillon/Frisco/Silverthorne there are plenty of dining options that are more reasonably priced. Dillion Dam Brewery, Pug Ryans and the Pour House are all in Dillon, towards Avon there is the Vail Brewery and there are lots of dining options in Avon.