First of all, I'm curious as to where you are that you can't get any digital (aka HD) channels, but you do get analog channels. I get digital channels significantly more clearly than analog channels.
As people have said, in the United States, conventional analog TV signals WILL go away on January 30, 2009. That means if you buy an analog-only tuner for the primary purpose of watching analog broadcast TV, it will be useless in less than 2 years. You can still use it to watch analog cable (until the cable companies decide to stop supporting it. They are under no mandate past 2009, they just know that to immediately obsolete every single "Cable Ready" TV made in the past 20 years would be suicide.) You can still use it to watch VHS tapes, game consoles, etc, connected through it. But the TV tuner part of it will become useless in less than 2 years.
The Hybrid, on the other hand, has both a 'less featured' analog tuner plus a digital tuner. You can pause live analog TV on it, but it is really 'freeze frame', and doesn't have time-shifting capability unless you are recording at the same time. (I only have one channel in my area that I watch that is analog-only, so when I watch it, I just always hit 'record' so I get the same functionality as I do on digital channels. I just delete the recording afterward.) Of course, it does fully support 'scheduled recording' of analog channels, for later playback, just fine. It will even auto-export it to iTunes as a TV show for you.
As for recording power needed, I'm recording an analog show right now, at maximum quality, (DVD compliant MPEG-2,) and EyeTV is using 120% of my 2.0 GHz Core Duo. That means a single-core computer wouldn't be able to do it, but any dual core should handle it. You won't have much processing power left over on a dual-core 1.66 GHz machine, but you should get full quality. Merely watching analog TV uses only 20% of my processor, on maximum settings ('Best' quality with 'Progressive Scan' deinterlacing.) Watching high bitrate full 1080i HD uses about 80%, so it should be marginally watchable on a single-core Intel, and fully watchable on even the slowest dual-core Intel. If I drop analog live quality to 'Good' and no deinterlacing, processor time drops to 5%, and recording at lowest quality (Video CD compliant) is at a lowly 28%.
Oh, and if you want to play a video game system through your EyeTV, the Hybrid is the way to go. It has zero lag, since it is just spitting out the raw data, as opposed to the 200 and 250, which have to encode it for transfer, which adds lag. (I play my GameCube (LEGO Star Wars II, Enter The Matrix, and a couple other games,) through it all the time. And hooked my Wii up just to see if it was playable. it is.)