Mouse and Keyboard is the preferred method, I think. It doesn’t really support joystick; you can’t actually configure joystick specifics (axes, buttons) in the game’s control panel. And the ships are turret ships that shoot in all directions, so the ability to “look around” with the camera is important. Game isn’t a dogfight game; you order your ship (like a captain) to approach, orbit, warp-to, or otherwise navigate itself to your target or other points of interest, you lock targets, and you activate weapon systems, shield/armor systems, electronic jamming, etc., with the computer actually doing the aiming and the hitting.
Voice chat is common; the game has its own voice-chat embedded into the (text) chat channels, but of course that has the disadvantage that if the game crashes you also lose the chat. So most player corps use voice chat; Discord is popular, also Mumble, TeamSpeak. You usually get details once you join a group.
EDIT: EVE doesn’t allow user interface add-ons or script macros (like WoW); you will get banned if you use any bot, script, macro, or program to automate things. AND, when you open the game for the first time, the user interface isn’t arranged in the best possible configuration. So you should spend some time to enlarge that Overview so you can see details, and reposition the various windows as you see fit. Hit ESC to access the EVE Control Panel and look at the options there, esp. keyboard shortcuts.