jake - The answer to your question is a big fat 'it depends'.
Your CRT televsion (no model number given) is likely a interlaced only display, but may display at 480i, 480p, and 1080i. It is very unlikely that it displays at 720p. (yes, it accepts 720p, but don't confuse that with it actually displaying at 720p)
Anyway, with Sony's reputation of not having some of the best scaling or deinterlacing it would probably make sense to get a DVD player like the Oppo, Panny S77 or S97, and hooking it up via HDMI/DVI cables to your TV for best results.
Especially if your DVD player is so old that it doesn't have progessive scan output.
I would recommend a new DVD player, and please, always include an exact model number for any product you are asking about as it will help others make the best recommendations for you.
In comparison, a good Panasonic plasma may have excellent scaling and deinterlacing - plasmas, LCDs, LCoS, DLP are all progressive scan formats by their nature. CRT is the only mass product that displays interlaced signals as properly interlaced.