Mac Pro 1,1 with nvidia 7300, good for EyeTV?

I've never owned a Mac Pro, but can tell you that satisfaction with EyeTV high def playback is largely CPU driven, i.e. the software is so poorly optimized that it usually comes down to having enough processor punch. So, your video card w/ 256 MB VRAM will not be a limiting factor and in terms of CPU, what you can do is look at bench scores for your model and see how it compares to other models:

http://www.everymac.com/mac-benchmarks/index-mac-benchmarks.html

a quick look says your 2006 Mac Pro will outperform all of the 2010 Minis and is equal to or better than almost all of the 2010 C2D MBPs. That suggests you will be fine with EyeTV. What you mainly need the CPU punch for is to deinterlace 1080i programming at EyeTV's best setting, called 'progressive scan,' rather than toggle down to its second best setting called 'motion adaptive.'

And if for some reason you're not happy with EyeTV playback, you can just play all your EyeTV recordings back with XBMC, as I do.

It really is sad that hardware accelerated MPEG2 decoding is not exposed by Apples public API's, but clearly they have a financial reason to never expose this functionality which sits unused in every video card they install in a machine. Its called iTunes. Why would they want you watching and recording content on your Mac when they can sell it to you and make a profit off it? In this case I much prefer the more open MS programming API compared to the limited Apple API.