Modern day PC game controllers: keyboard, mouse, game pad, keypad, joystick, HOTAS, HOSAS, voice programs, stream deck, head tracking, eye tracking, and I am sure other types of game controlling items and of course headphones with mic for the game and voice chat (Discord, Teamspeak, etc outside of game).
All modern PC based games can be controlled with keyboard and/or key pad and mouse. Many will configure for a controller (like from an X-Box and other game consoles).
Everything listed above can be used in Star Citizen in some combination. For example, I use a Corsair K100 keyboard, Redragon K-585 DITI key pad, Corsair Scimitar Elite mouse, Thrustmaster T16000 joysticks (dual, for 6 DOF), TrackIR V5 head tracking, an Amazon Fire HD 10 for Gameglass and sometimes VoiceAttack and looking to get an Elgato Stream Deck. Most of today's games do not require as many controllers, just a keyboard and mouse or game controller
As far as the machine, well that will depend on what your playing. The current top of the line consumer game machine would be an AMD Ryzen 9 Gen 3 5950X 16 core, 32 thread CPU, (an AMD Threadripper can be substituted) with at least 32GB ram (recommend 64GB game dependent) with an AIO Liquid cooler, an AMD RX 6800 8GB or better GPU and at least one NVMe M2 PCIe 4 1 Terabyte SSD (HDDs are cheap but once you go SSD you never go slow). The internet connection should be at least 500mb or a 1 Gb most games are now DLC and are 20, 30 to 100GB in size.
I stopped using Intel CPUs years ago, so not familiar with them.
There is much more but the above should be enough to help you plan a setup.