I don't have an X1300 but I do have a Radeon 9550 and a 9800 pro. They both work great on my 27" TV.
If you want the best picture quality, the thing to consider most would be how you will connect your video card to your TV. If you plan on using the composite inputs on the TV, it may not matter if you have an X1300 or an X1800. The composite signal will be playable, but there are better ways of outputting your signal to your TV.
Next up is S-Video. This is probably what most people use. It is better than composite signal but there is better still.
I don't know if you have gotten your TV yet, but if you want the best picture quailty for classic gaming using a traditional TV, get a TV with RGB component inputs. If you do a side by side comparison of the picture quality, the S-Video and the composite will look absolutely yucky compared to RGB component connection. You will need a DVI to Component adapter for your card, and a set of good quality RGB component cables.
Most of your 27" curved-screen TVs will have composite and S-Video, only a few of them will have component inputs.
I bought a 27" Sharp 27C240 for $160 at hhgregg that I was gonna put in my cab, but my wife liked the TV for watching movies so she did not want me to put it in a cab. I tested it out using S-Video and composite and the picture quality was decent. Worked great for playing dvd movies from the PC.
But I needed another TV for the cab, so I convinced her to let me get a new one. I ended up getting the 27" JVC AV-27530 from hhgregg for about $190. It had RBG component inputs. I read about using these and that the quality was superb, so I wanted to try it at least.
The picture quality is indeed superb.

... RBG component inputs beat the pants off of S-Video and composite when it comes to classic games. Absolutely awesome!!! I was so glad that I went with this setup.
I don't know if you are using a TV you have already, or if you plan to buy one. If you have one already that only has S-Video and composite, then it will be decent and certainly playable, But if you buy a new TV, definitely try to get the RGB component inputs, it is worth the price difference...IMHO...
If you have the card already, you could test the picture quality on a TV you have around the house, or on somebody else's TV.
Good luck on your first cab...
