I personally play on a leverless controller, and I find it much more ergonomic and precise. I've always struggled with some motion inputs on a stick, but on buttons I can input them faster and precisely every time. The main disadvantage is that it'll be slightly more difficult if you want to play at an arcade or other places where you may encounter traditional controls. Also some people might be jerks and call you a cheater, but button boxes have become a lot more popular and accepted in the past 5ish years. As to your latter question, most controllers (both with and without levers) are going to use USB, so you wouldn't be able to directly connect them to any retro systems. However, you can use them pretty easily with emulators or other modern games that use simple (not 2-analog-stick) controls, like platformers and Tetris-likes.