Most of the all in 1 apps are not really that good when it comes to the odd DVDs (and there are a lot of those).
Therefore I favour a more complex approach, it takes about 5 minutes setup time all in all but.
Ripping:
DVD Decrypter +ripit4me frontend (search around doom9 forums or if you have to I will sort out a mirror:
http://forum.doom9.org/ ) works most of the time and DVDFab takes the few that do not.
http://www.free-codecs.com/download/DVDFab_Decrypter.htm
Now some nice vob, ifo and bup files appear. Here I would reburn or use DVDShrink/rejig, voblanker and all the other assorted DVD tweaking tools but we are going to AVI (not to mention that is a whole other area).
You want something to pull apart the vobs into something nicer.
DGMPGDec is it:
http://neuron2.net/dgmpgdec/dgmpgdec.html
This will allow you to make an avisynth script (not hard once you see how it is done, the helpfiles there are great for the initial stuff)
You can add a resize and filters here if you want but most DVDs do not really need it (if going for a standalone check what resolutions and other stuff may be needed, XBMC is pretty bulletproof if you are going that route).
Now you can do just about anything with it when it comes to encoding it, I like megui but there are some more simple apps if AVI is all you want.
Megui can be grabbed from
http://x264.nl/
Virtualdub in pretty much any of its incarnations will do here too if you can find codecs for it.
QuEnc is also good (I use it mainly for DVDs and DPG but it does other stuff too):
http://www.bitburners.com/quenc/
If you are after MKV megui does basics but MKVtoolnix does the lot:
http://www.bunkus.org/videotools/mkvtoolnix/
Finally subtitles:
DVD subtitles are essentially a string of bitmaps so you need to run OCR on them.
Subrip:
http://www.free-codecs.com/download/SubRip.htm is as good as any.
Subtitle workshop is what I suggest using to tweak them:
http://www.free-codecs.com/download/Subtitle_Workshop.htm
And if you happen to reburn to DVD this tool is great for tweaking subtitles (I use it mainly to get rid of the insipid yellow used on a lot of anime DVDs and typos (or use of US English) but it does get far more in depth if you need it to):
http://www.free-codecs.com/download/DVDSubEdit.htm
Edit: To add to CockroachMan gordianknot is a bit old but it is rock solid (its more automated cousin autoGK actually mirrors my own methods above fairly closely).