You are pretty much wide open for video cards as just about anything out there should handle sd video fine. You might as well build it with HD capabilities in mind too though. Unlike gaming, you don't have to spend a fortune to get a video card that can play HD video well. The 3450 that beef barley starts at about 30$. Any ati 2***/3***/4*** series will do it fine. It wouldn't hurt to spend a few more dollars if you like and get a mid range 4*** series card. You could even get a 4830 starting at about 100$ (second highest model card in the 4*** series). As far as outputing direct to the tv, all you might need is a simple adapter (and many video cards include them).
For hard drive space, you need a LOT. Figure a few GB per movie. I would probably start with at least 2TB. I have about 2TB on my htpc, and you would be surprised how fast it fills up ripping movies (even more so when you start loading it with tv shows etc).
As far as format and ripping, does 1 click dvd copy create a video_ts folder (or a named folder with a video_ts sub folder)? If so it is ripping it in standard dvd format. Its the same I get ripping with dvd decryptor or anydvd ripper. Nero will play straight from ripped video_ts folders. I'm sure there are other programs that can do it too but not all will. You can compress to get them a little smaller, or you can convert to a video format like h.264 and get a lot smaller without much if any quality loss. I have been converting to h.264 with about 1GB file size and have been happy with the results. I have heard someone else say that you need to get closer to 2GB file sizes for large HD tv's to get best quality possible. The problem is, ripping takes 5-10 minutes, converting to h.264 takes hours. You still need room for a lot of ripped dvds so you can start using right away, while you are converting.
I'm running windows xp on all my machines so I cannot really comment about vista much. Your options for software are windows media center (available on xp media center edition, vista home premium, and vista ultimate). If you are building a computer, you need a media center remote and receiver. This was just the cheapest one on newegg. There are many different brands and models available.
You can get a computer remote (doesn't require windows media center). Some may also be able to control windows media center.
Here are a few.
you might find more on remotes here.
many will come with their own htpc front end. Some claim to be able to control many programs. I have the stream zap one, and it claims to be able to control dozens of programs. Personally, I was disappointed with it. I only tried it with the few programs I use, but not all functions would work. Even if every control works except for fast froward and rewind (that's what it did with nero home), you would be surprised how annoying that gets. Also, be aware, if you use a programing remote like a logitech harmony, you should be able to manually program it with commands for ir computer remotes (you will need to buy the computer remote to get the receiver, software, and have the remote to teach the commands though).
I think the biggest issue here is to find the software you want, and find a remote that works with it. I also tried this one. It works fine with the media center pc in the bedroom, but as far as controlling other software (on my htpc in the front room which is not a media center pc), I wasn't really happy with it.
Higher price doesn't always get the best.
I recently installed this one
hopefully it will work better. There are more advanced versions of that one too.
Software. Google htpc front end. that is the software that will run the computer. It is basically a graphical front end designed for media (and designed to be seen and readable from across the room on a tv). There are many of them out there. Nero comes with one. Most computer remotes (non media center ones) come with one. Many tv tuner cards come with one. There are plenty others too, both free and paid ones. The problem is finding software you like, and getting a remote that works with it. You might also want to throw a tv tuner card into the equation (so you can watch and record tv from your computer). Compatibility with it, your software and a remote may matter too. Here is a thread about front ends
And a list of some other front ends
I would be concerned with their ability to play a ripped dvd as that is your primary need.
This is a bit of a long read, but you may want to glance through it about hardware.
That probably didn't answer all your questions, but hopefully it will hep point you in the right direction.