Chicken – use a regular pan instead of a cast iron skillet

Yes, you don't have the edge of a pan in the way when going to flip things, but it also means that you don't have a mass of metal there to add as a heat sink, which can help dramatically when pre-heating your pans, as they'll be evenly heated across their bottom more quickly (at least, compared to something of the same material, such as a cast iron skillet)

More importantly, in my opinion, is that without the sides, you don't hold in moist air, so when cooking things like hash browns, you can get a better crust on 'em without steaming them.

A normal frying pan would probably work just fine for you. If you use a non-stick pan you'll tend to get less crisping on whatever you're cooking and if you plan to deglaze to make your sauce you'll get less yummy bits to work with. However, I've used non-stick cookware to make a lot of things (porkchops in white wine sauce, yum!) and it usually turns out fine. Just be aware, too, that if you're using non-stick cookware to fry and your recipe calls for any kind of cooking oil, you should probably use a little less to avoid that gross oil-soaked effect.