MKV is a great container format and MakeMKV is very popular (and for good reason). It really gets down to what you want to do.
For me I just put in a BD, and let MC do the lot (rip, import, tag, coverart etc). It is easy and it works (unless you are trying to save as much disk space as possible). I have an exact 1:1 copy of almost 1,000 BD ripped like this and not seen any downside. MC Support for BD is very good so you can access all the titles, streams etc. Like with all media you can then play/stream the rip just fine to MC, Remote clients, and MC can make a portable version for a target device if needed. The only three BD features you don't get is native BD Menus (you do get MC's), Chapter Names, and 3D support (if you care about either).
Oddly - I find DVD harder to manage. Thankfully, I have only a few DVDs (mostly Music DVD) and for these I have ripped them using 3rd party tools into a file format as MC relies on the MS DVD Navigator filter and it can be clunky.
With 3rd party ripping tools you need to think ahead on what you want to keep vs discard. Most seem to try to discard content they don't think they will need (audio tracks, bonus features, alt endings etc). Not that it will happen much, but I'm glad I've kept full copies as for example we normally watch with an English Audio and forced Subtitles on, but we had an Italian Exchange student for a couple of months so sometimes the preference was for a Italian Soundtrack with English Subs.