Hey Napoleon - welcome to the AP forums.
CPS3 is a cool platform, and I think once you get all setup, you'll be pretty happy with it. The background update mod that
@riiya has produced for CPS3 Third Strike really improves the look of the game - highly recommended you try it with the Darksoft CPS3 Multi.
Let's talk SuperGuns.
As you likely already know, the CPS3 PCB is designed originally for a JAMMA arcade cabinet with a kick harness connector to provide the inputs for the three kick buttons. CPS3 also supports stereo Q Sound as an option by connecting amplified speakers to the RCA line level connectors. Ideally, you'll want a SuperGun that (A) will accept a JAMMA board, (B) provides kick harness support, (C) has a high-quality, adjustable power supply so that the CPS3 board is safe long-term, (D) is safe for the television or upscaler that you connect it to.
I'll be blunt - there's a bunch of SuperGun options out there right now and most of them are garbage. Many SuperGuns either don't attenuate the video output properly (dangerous for your TV or upscaler) or they doesn't provide safe, consistent power (dangerous for the CPS3). Some of them (like the ones made by Electroelectronik) have been known to have bad grounds that can burn out the controllers plugged into them.
The SuperGun on Ebay you linked to is one of the garbage ones. This SuperGun doesn't support the Capcom pinout kick harness so you won't be able to hookup the kick buttons for a CPS3 board without coming up with a custom connecting harness. Secondly, they don't say what kind of power supply they use - there's a dial for adjusting the power from 5.15V to 5.30V, but even 5.15V is too high. JAMMA boards, including CPS3, should be adjusted to be as close to 5.0V as possible. Trust me - stay away from this SuperGun.
There are a few quality SuperGuns that I can recommend that will meet your needs:
1) The Home Arcade System (HAS) is created and sold by
@RGB on this forums. You may have to wait a bit to get one, but I think everyone on these forums agree that the HAS is one of the best SuperGuns money can buy. There's a thread (with links to the waiting list) about them here:
https://www.arcade-projects.com/threads/home-arcade-system.332/#post-2521
2) The MiniGun was engineered by
@Frank_fjs on these forums and is available as an open design that anyone can build. I'm sure someone on the forums here could assemble one for you. Maybe
@hatmoose ? Thread is here:
https://www.arcade-projects.com/threads/minigun-supergun-an-open-source-supergun.9408/
3) The Axun Workshop SuperGun Mini is engineered by
@axunworks and supported by
@drfunk2k . You can order it here:
https://www.axunworks.com/product-p669501.html
The HAS SuperGun has Composite TV output as an option, but the MiniGun and SuperGun Mini do not. As long as you pick a good converter though, you should be able to get Composite picture without lag. Arcade boards don't output native composite so SuperGuns that have Composite output are likely using a powered converter to provide that functionality anyway.
@axunworks announced that he's working on a device that can convert RGB SCART or VGA Input into Composite or S-Video output. I strongly recommend you pick up one of his converters when it releases if composite video is important to you. Details here:
https://www.retrorgb.com/rgb-to-composite-s-video-converter-announced.html