When I last had CRT TV next to PC in 2003ish, doing TV out from my GF3 on an Athlon XP system. I preferred the 800x600 in game, any res was hell for text and desktop though, so best to have even the worst 14" LCD for admin and management stuff rather than expecting to rely solely on TV.
A major problem with finding good TV out capabilities in a card is that it varied by specific card model per specific card manufacturer. So you can't just search the GPU and get a list of ones that will work... gotta eyeball them for the socket, ask the seller if they have the possibly unique dongle for it. There are pretty much no good reviews around for video out functionality for any "normal" cards, though some specially targeted home theater cards with all the bells and whistles did get a review or two that did. The reason for this appears to be that cards were always reviewed as preview models, with preview drivers which were "just the basics" and did not include the Video Out components/utilities necessary for these cards at the time they were reviewed. They were added to retail drivers. Also it appears that the right drivers may only be in driver packages from a year or two of release of the specific card and you may need manufacturer specific drives. So you need 70 series detonators for your video out to work, but oh no, maybe they were broken for a later game, and an 80 or later release fixed it, but guess what, no TV out drivers.... it's a mess.
Unicorn herding operations are proceeding, but all the totes of hens teeth and barrels of rocking horse poop give them plenty of hiding spots.