Here are some of my favorite controllers for FIGHTIN' GAMEZ. We'll start with PADS.
Neo Geo Controller:
The best of the best if you ask me with its only fault being it lacks six buttons which makes it only good for SNK fighters but this is one of the greatest controllers ever created. Comfortable to hold, great D-pad that has microswitches, buttons are quick and responsive, if you can find a modified Neo Geo controller that works on modern hardware and you like SNK games this is the default way to play.
Sega Genesis 6-Button:
The controller a generation grew up with and one of the best arcade style pads you could ever get, the Sega Genesis 6-Button was a thing of beauty. I long considered the Genesis officially licensed controllers to be among the best to play with since they fit into your hand easily and the buttons are just the right size as well having a fully rotational D-pad that makes doing more complicated motions much easier. I like the Retro-Bit remastered version, but DO NOT get the one advertised as 6 buttons on the box. Get the 8 button one with USB. The 6 button one only works for actual Sega products so you'll look like a caveman trying to put it into your PC. The extra two buttons are on the shoulders and it comes with an appropriate mode select in the middle so you can actually use it universally for modern shit.
The Original Playstation Controller:
I've been a long time advocate of the OG PS1 controller which I've always preferred for games like Mortal Kombat or any other with committed directional inputs (no motions needed). The lack of analogs make this a very comfortable fit and this is one surprisingly durable controller. I still have my very very first one from '95 that functions just as it did back then, it has survived numerous hammerfists and tossdowns in disbelief and unfettered anger. Another important note is the L2/R2 buttons are the same as L1/R1 meaning they aren't retarded triggers like in the PS3/PS4 era so it's much quicker response time. Another benefit if you have big oaf-like hands is no analog means no accidental collisions with your thumb to fuck up your inputs.
ARCADE STICKS:
Neo Geo Arcade Stick Pro:
This came out in the last year or so and is probably the best entry level arcade stick if you want to get serious but don't want to carve out your organs to pay for something more expensive. It retails around $130 USD and is both a console and controller. It has 40 preloaded games from SNK's library including all the good fighting ones but it can also be used as an actual arcade stick for any other game. It's pretty much a convenient "all in one" sort of arcade stick that gives pretty good value considering the price, it also doesn't adhere to the Neo Geo arcade cabinet design so you got 8 buttons making it usable for all fighters. The buttons/parts it uses are not of Our Lord Sanwa, but they're of good quality and won't fall apart on you after 3 months like those shitty $50 sticks will. You can also switch the buttons/stick out if you want to replace them fairly easily, I'm not sure if it works with PS4/XBox One since I don't own those consoles but it works with PC seamlessly and has multiple mode switches on the side.
If you do play the games provided, some games, notably King of Fighters '99, may seem like they have a delay or don't respond to your commands on something like the character select.
This is not a problem with the hardware/stick itself, this has been a known issue for that particular game's emulation. You should be playing '98 or 2002 or Garou anyways. Bao is a faggot character.
Bat Top Sticks:
What you have here is a Street Fighter IV Tournament Edition arcade stick with one very big difference: the usual ball-top stick is replaced by the bat top. This isn't a usual thing you'll see on most arcade sticks but if you've ever lived in NA and played arcades then chances are you grew up playing with this style on most arcade cabinets you ever encountered. This is purely a preference for me as it is what I'm most accustomed to and feels most natural. Some people will say some dumb Japanophile shit like "BUT BALL TOP IS MORE PRECISE//BAT TOP USES MORE MUSCLE MOVEMENT." Look fags, if you care about energy exertion so much then chances are you're dying IRL if playing with a bat top actually exhausts you. There are some ready made arcade sticks that use bat tops but in my experience I've had to switch out ball tops with bat tops.
The big rule when it comes to arcade sticks is this, check if it has Sanwa or Hayabusa parts. The Sanwa parts are genuine arcade buttons, the ones you'd always hit as a kid. Hayabusa are new style, usually carried by Hori if I remember correctly, but they're still high quality. Whether you want the button tops to be convex or concave is you to decide, I personally don't give a shit. You want Sanwa or Hayabusa because they can endure months and years of abuse and are 'springy' and receptive immediately. I don't mean you can all of a sudden uppercut your buttons over and over and expect them to still work, but when it comes to pressing them and expecting a proper reaction without the worry of them being delayed or outright jamming/falling apart then Sanwa/Hayabusa will last you a good while.
A good Sanwa arcade stick that's of quality without breaking the bank would be the Qanba Obsidian.
Anyways that's pretty much what I like to use or personally recommend. Now go learn how to bunny hop.