I was also thinking instead of buying a PC to dedicate as a media server, buying a HTPC and using Kodi as the media player program. I recently was trying out the Kodi media player program on my PC and I like it. There is no need for transcoding with Kodi when using MKV files with lossless audio formats and I find that Kodi's interface works pretty good with my Xbox one controller even though I prefer to use my Harmony remote instead if it's possible. I'm not sure if my Harmony remote would work with Kodi. Whether I dedicate a 2nd PC as a media server or a HTPC, it will be the same pre-built PC I'm considering on buying, the Dell Inspirion with the i3-4150 and Intel HD 4400 Graphics. Will that PC handle 1080p MKV's with lossless audio?
You don't need much to do that. Heck, I was streaming 1080p MKVs with an Intel Atom processor a couple years ago. Granted I had a dedicated video card to do the decoding of the video, but the only reason I upgraded from the thing was because using the GUI to pick what to watch was slower than I liked; videos all played fine.
Nowadays, any of the Intel i3 (or less) series of processors will take care of you. Use the onboard graphics with 4 GB of RAM, and you will be just fine. I do recommend an SSD if you are going to have much of a GUI with it (like XBMC, or some variant like Plex) especially if you are making something that needs to pass the "wife factor" of ease of use and speed.
As for a dedicated Plex Media Server - yes, it's a good thing to do in my opinion. I have one that runs plex from a closet downstairs. How powerful it needs to be depends on your use case. If you won't depend on it for transcoding media, and won't have many simultaneous feeds going, any old PC will do. If you have a lot of people who could use it at once, or you need to transcode your media to different formats for different devices, a better CPU is better, since the media server does all the work. The reality is, when using Plex, the server is the one that does most of the work. Your clients usually don't have to be powerful at all.