Your basic fork in the road when it comes to graphics cards is to go Analog or Digital. Every new card is digital only. The last Analog card was the AMD R9.
Analog is simpler but obviously not as powerful as the newer cards (not really an issue for almost all arcade games if you are using a CRT). The newer digital only cards will require a digital to analog converter like the one you linked above.
If it were me starting out, unless there was a real reason to do so I would buy a card with Analog out. It’s simpler, and cheaper. Analog out comes with any VGA connection (don’t be confused with the newer AMD computers that offer VGA from the motherboard, they won’t work), and any DVI-I connection, not DVI-D.
From there you will need either a DVI-I to component, or VGA to component cable to plug into a Transcoder you will need to buy since you indicated you aren’t interested in modifying the TV.
Once you do all that you just need to setup all the software.