You may be able to use your dxr2 card if you use mplayer as the dvd playing application (there seems to be a xine dxr2 plugin--but it's elderly and doesn't look like it's been continued), not sure about ogle. Not sure how menus or overlay issues are handled though.
A lot of people like nvidia cards due to the availability of linux drivers for them. The FX5200 has practically become a standard. An important consideration when choosing your card will be how you plan to hook it up to your TV (VGA, DVI, svideo, composite) and making sure you have that type of output on it.
With only basic analog cable Hauppauge makes good cards (the PVRx50, PVR500, there's now support for the PVRUSB2). If you are worried about future proofing your investment, I don't know if myth supports the NTSC use of high def cards. The linux tv wiki
http://www.linuxtv.org/wiki/index.php/ATSC_cards claims that the drivers for the HD3000, the Fusion HDTV3 Gold-Q, the Fusion HDTV3 Gold-T, the Fusion HDTV5 Lite, the Fusion HDTV5 Gold, the ATI HDTV Wonder support both NTSC (for now) and QAM (for later). But that's not saying myth supports them or that they are good NTSC encoders either. Because these cards are sold primarily for their high def usage, the NTSC components are probably not so good.
Another option you might consider is the Plextor TV402 product. I'm using the Plextor M402 one (no tuner) and it's working very well to capture from my sat tuner with minimal CPU.
The advantage of these cards I've mentioned is that they don't take much CPU. With 1.4G, you could probably even go with a frame grabber if you wanted to, though through judicious use of online shopping, you can get an affordable hardware encoding card.
If you use a hauppauge pvrx50, pvr500, pvrusb2 card they may come with a remote (depending on what incarnation you buy) which tends to be supported by linux. Other than that there are quite a few (streamzap, ATI) and a number of people use a wireless keyboard and programmable remote.
To rip DVDs and put them back together? A dvd burner would help.
You'll need a network connection to the internet in order to get zap2it listings (if you're in the States--if you're not, ignore everything else I've said as I don't know a SCART from a CAM). I've heard of people using dial up for this even. I use a wireless connection for this purpose.
There are plugins for weather (MythWeather), news (MythNews), mp3s (MythMusic), and pics (MythGallery). You might hunt around there might be something for netradio too.
Good luck.