Ahofle, thanks for the mention. Yes, reading through that thread will be a help. Bear in mind that it's a little old though, so there is a lot of talk about Soft15kHz. Notice the updates in the second post (which need to be updated again at this point).
The technical discussion there is still valid, but just bear in mind now that CRT_Emudriver is a much better option than Soft15kHz, and everyone with a CRT ought to be using GroovyMAME at this point.
You're not likely to have success with "TV-out" from a video card, regardless of format. You're not getting the full benefit of a CRT without running native resolutions, and no one has yet found a card that's capable of doing this through the TV-out port. If you can confirm that you've found a card that can do so that would be interesting, but you'll most likely need to use the normal VGA out from a CRT_Emudriver-compatible card and run that through a VGA to component transcoder.
See my recent posts near the end of the thread about the current availability of CRT_Emudriver-compatible video cards and VGA to component transcoders.
As for a TV, if you want to run native resolutions you'll need something with a component input. Be careful though, you need something that's 15kHz-only, meaning something that can NOT display 480p or higher. Otherwise, it won't be able to display native arcade resolutions from MAME, 90% of which are around 240p, it will just upscale them to 480p or more before displaying them. In the US, a Sony KV-27FS120 is a good bet. They have a great picture for MAME, and can commonly be found in most areas on Craigslist for very little money. (I'm assuming you want to stick with a 27" tube. For others reading this, there are also 20" and 24" sets in the KV line.)