Cooking spray will not damage stainless steel the way it will damage nonstick. It does, however, leave a hard to clean residue.
To help keep foods from sticking to stainless steel pans, always pre-heat the pan on low to medium low. Then add a little oil and let the oil heat up. Cold food sticks to the pan worse, so take your food out of the fridge about 20 minutes before you cook to take the chill off.
When you put the meat into the pan, try to resist pushing it around with your spatula. Just let it sit. The meat will start to release a bit when it's ready to be turned.
When you take the food out of the pan, leave the pan on the heat and pour a glass of warm water into it. The bubbles and steam will help clean the pan. While it's bubbling, use your spatula to scrape up any bits stuck to the bottom.
Don't rinse a hot pan in running water, it'll warp. Let the pan come to room temperature before washing it. Barkeeper's Friend powder cleaner is great for taking off the residue or stuck on bits. ($1.79 at Target)
And keep a nonstick skillet or two around. Starchy foods and eggs are a million times easier in nonstick.
Hope that helps.