If you're looking for tri-ply cookware, I've found that the cheapest are usually either Cuisinart Multiclad Pro, Henckels Classic Clad, or Sam's Club Member's Mark (only comes in sets at Sam's Club, may not be available at all clubs)
Cooking just for yourself or for other people regularly?
1. Cast Iron Skillet: Well, start off with a cast iron skillet for $20-30. This will be a workhorse. Baking. Roasting. Broiling. Frying. Saute-ing.
2. Saucepan: 2-3qt. Pasta, soups, etc.
3. Stockpot: Any stockpot with a thick metal base will be fine. You're only going to be boiling or simmering in this thing. You can buy steamer inserts that go right into these stockpots. Hell, Wal-Mart might have them.
4. Good chef's knife and a honing steel.
Cookware can be very basic. You don't need anything fancy or glitzy. The quality of the food is determined by the cook. I keep on thinking of places like China or Vietnam, where the food can be absolutely delicious. Do you think the cooks there use fancy polished tri-ply cookware? Heck no.
As for food sticking, don't use such a high heat. And if there is some food residue, try to scrape and clean it off under water while the pan is still hot. If you've really cooked the food into the pan, use Barkeeper's Friend to take it off. BF is amazing.