I ripped all my DVDs and then converted them all (using handbrake) so that I can play them in iTunes. That was a while ago. They (along with everything else) sit on my NAS and play through my apple TV. My advice:
Decide what you want to play them on first – that will determine what format you need (or don’t need) the files to be in. It’s been a while since I looked into this, but I think if you use MKVs, you’re not actually “converting” them as such, just “repackaging” so it’s much faster.
I use Plex, but Infuse is very well regarded if you want to use an apple TV as the client – but if you are not wedded to apple, their are lots of options.
As others have said – I wouldn’t bother ripping/encoding if I was doing it again. I would get a couple of months VPN subscription, find a decent torrent source, and just download new versions of my files in the format I wanted. If you own the films you are downloading, I see no ethical issue with this.