Most of the salad and frittata recipes with shrimp call for cooked shrimp. You can, of course, buy cooked and peeled shrimp. But I believe that raw shrimp, cooked earlier in the day, are much fresher, tastier, and have a better texture.
The raw shrimp in the seafood case at your local market have almost always been previously frozen and were defrosted before they were put on display. Indeed, if you ask to buy 2 pounds of shrimp, the person helping you may well suggest that you might want to buy one of the bags of frozen shrimp, explaining that they are the same shrimp that are on display. Getting the shrimp frozen and defrosting when you are going to use them guarantees that the shrimp are as close to fresh as they can be. I usually keep a bag of frozen shrimp on hand in the freezer.
The choice of unpeeled or peeled shrimp is a matter of personal preference, convenience, and what is available in your market. Cooking unpeeled shrimp gives them a bit more flavor from the shell (shell the shrimp after cooking), but the peeled shrimp are certainly less work. I go both ways, but I really try to at least find shrimp that have already been deveined.
Frozen shrimp can be quickly defrosted by putting them in cold running water for about 5 minutes. Definitely defrost completely before cooking, or they will cook unevenly. To cook, put the shrimp in a pot of boiling water, bring back to the boil, and cook for a couple minutes until the shrimp are opaque, pink, and have started to curl up. (Or follow the instructions on the bag or use your own favorite method. Some people put the shrimp in the boiling water, turn off the heat, and let them cook that way.) However you cook the shrimp, do not overcook, as that will make the shrimp tough.
As to the size of the shrimp, that isn’t critical and again is a matter of personal preference. For frittatas, you will want small pieces, so all but the tiniest shrimp will need to be cut up anyway. For salads, I tend to go with 31/40 shrimp, those officially termed medium large or large, though not what most people would consider big shrimp. I think they look nice on the salad and are fairly easy to eat. But feel free to go smaller or larger. Just remember that if you are buying unpeeled shrimp, the smaller the shrimp, the more you will have to peel.