I'd like to rip my DVD collection both to free up some shelf space in my living room. I have a PC hooked up to my television, but it has very little disk space, so I'd like something I can view over my (wireless) network. Am I best off going with copying the VIDEO_TS folder or converting to AVI files or MPEG4? If I convert to MPEG, what is the minimum resolution I should use?
Which codec? DVD ripping software exists abundantly. Converting to MPEG-4 gives you two options:
Which software? As always, if you want to rip DVDs to either MPEG-4 Part 2 or h.264, I suggest the famous Handbrake, free, open source, cross-platform. With h.264 selected, you can choose to rip your video as .MP4 or .MKV container. Choose whatever you like better. MKV is the most widely used container these days for h.264 video.
Settings: When encoding, you need to play with the settings. Encoding takes time, and you might want to start out with the presets ("High Profile", which offers the best quality).
Resolution: What resolution you use will depend on your TV. Remember though that video DVDs offer a maximum resolution of 720 × 576. There's no "magic conversion" that will provide you with a 1080p video from a DVD. Just go with the native resolution and don't scale the video. It will hurt your quality, because you're re-encoding an already-encoded video when you're ripping it.