Gyros are traditionally slow-cooked on a spit. This is tricky to do at home. "Tex-mex" gyros are traditionally heavily-marinated meat skillet-cooked with veggies. This is the simplest thing ever. Basic advice is to use more seasoning than you think is reasonable, cook hotter than you think is reasonable, recognize that a little carbonization is damn-near mandatory for decent street food and tzatziki is important. I make mine with greek yogurt, fresh lemon juice, tahini, salt, pepper and dill. Some people hate dill. I am not one of them. Use your judgement.
Steak is hard to fuck up. It's pan-independent. That said, I don't pan-fry steak. "Meat for meat's sake" dishes I grill whenever possible. The easiest, most basic approach to "cuts of meat" is to pat dry with paper towels, sprinkle liberally on all sides with salt and pepper, get as close to room temperature as is practical and then when you put it on the hot, don't fuck with it until it's half-done. Then flip it and don't fuck with it some more. That nice carbonization/maillard reaction wonderment doesn't happen near as nice if you constantly fidget with it.
Allow me to state for the record that I am not a member of the Slavish Adulation of Cast Iron Club. You're going to buy Lodge because that's what's available and Lodge doesn't cook that well. I also have a legit Wagner from like 1932 and guess what? It doesn't cook that well either. Despite arguments about how bomb-proof cast iron is, it's extraordinarily precious if you want the purported "non-stick" properties to persist. Copper-bottomed stainless steel, in my experience, cooks the most evenly.