MakeMKV is a fantastic ripper, and rips both Blu Ray and DVD. You can choose anything on the disc, including the FBI warning if you like
. You can pick and choose which audio track(s) to use, as well as captions. MakeMKV can also rip the audio into FLAC, which your Apple TV supports (more on that below).
There is only one caveat, and it may not be an issue for you. Blu Ray captions are in PGS format, and most playback devices (such as Blu Ray players or Smart TVs) will not display them from the MKV container. Depending on how you want to watch the movies, that may or may not be an issue. If your only playback device is the computer itself, then using VLC as your player works perfectly and displays all captions. PowerDVD may also work, but I can't verify that for sure as I don't use it.
I have a HTPC I built years ago. I have left it on Windows 7, as I like using the Media Center functionality. If you want to retain your HD audio (Dolby TrueHD and DTS Master Audio) you require a video card with HDMI out and feed that into an AVR. I still use an old ATI HD 5450 video card, as it has no fan so runs perfectly silent. The power supply and CPU fan are your other two sources of noise, but you can get them with low noise in mind. Depending on how many movies you want to rip, you will need a lot of storage. Put your movies on a drive separate from your OS. I currently have five 3TB hard drives, but could get by with fewer if the drives were larger.
Since you mentioned possibly streaming, I urge you to investigate Serviio. It can stream to virtually any device via DLNA, and transcode if required by your playback devices. While Windows itself has DLNA server functionality, it has little transcoding ability. Serviio doesn't have the ability to edit your metadata, like Plex can, it has far more functionality than other DLNA servers, and the device profiles can be easily edited for specific functionality.
You mentioned Apple TV. This player does not support MKV files, regardless of the video or audio codecs used. To my understanding, Apple TV would need you files in MP4 containers with H.264 video and for audio DD, DTS, AAC, MP3 and FLAC. It does not support either of the HD audio formats. Be aware that few playback devices support FLAC, so they would require transcoding of the audio.
Finding software that will rip your video into the desired container, using the desired codecs, is your toughest challenge. If you are satisfied with MKV (as I am) you can't beat MakeMKV. If you prefer to instead have them in a format that your Apple TV supports, you either need to find something else, or use MakeMKV then convert them with HandBrake (or other such software).