These are all fairly general questions that are beyond the scope of a single forum post. If you really want to get full on into video encoding on a PC, then you will need to do some extensive reading. I will try and answer your questions.
Firstly, lossless video takes up an incredible amount of storage space. DVD's themselves are not lossless, but encoded in a format called MPEG2 (forgive me if this seems condescending, I don't know how much you know already). To convert a DVD to a lossless video format would take up far more space than the original DVD.
The most common formats in use are implementations of a video encoding standard known as MPEG4. MPEG4 doesn't only consists of video standards but also audio and container standards. However, we are only concerned with the video for now. The most common implementations of MPEG4 are DivX and XviD, although others exist (eg. 3ivX). There is a free version of DivX with limited features, a no monetary cost version with more features, which uses adds that pop-up while browsing the internet to pay for itself, and a full pro version which costs US$19.95. The adds version and the pro version have the same feature set. XviD is a codec the devlopers are using as a learning tool. It is free to download the source code, but is probably illegal to compile and use in most countries. Binaries are available at sites around the web. It is probably illegal to download these in most countries to. However, XviD is
generally (and I stress
generally considered to be the most advanced codec of its kind. Ultimately the choice between DivX or XviD is up to you.
For information on how to convert DVD's or Tapes to DivX/XviD, you will have to read several of doom9's guides available at
http://www.doom9.org/guides.htm.
As far as a capture, I would recommend a Pinnacle card, prefarably one with Analog and Digital capture modes so that in the future you can capture video off of a digital video camcorder and edit it.
Please also note that converting DVD's or Tapes to video on a computer is illegal in many countries.