The 250W power supply (not CPU as your heading suggests

) will be plenty with if you use a low power CPU, mobo with on-board graphics and a single hard drive.
Your biggest problem will probably be getting the right output to connect to your CRT. If it doesn't have a computer VGA input then you'll need a graphics solution which supports component out or s-video, whichever your TV supports. Quality will be lower with s-video. Some mobo do come with this option, but you may need to have a separate graphics card - more power but you should still be OK.
Before you go down the 'simple' starter route it's worth considering that the majority of problems with HTPCs seem to come from using older pre-Vista hardware. Drivers may not be up to scratch, and this can give you all sorts of headaches.
If you're after WAF, then having a box that stutters and freezes or produces a picture that looks like sh!t won't help. Indeed it might turn SWMBO right off the media centre experience entirely.
So just be careful what you 'economise' on. The PSU is one thing, but other bits like the tuner, and even having a quiet case and fans, will be critical to the overall experience.
Good luck.