If you want it simple, look at OSMC or LibreElec. They are pre-packaged OS's especially for Kodi. LE is designed to be "just enough for Kodi" and is very light and locked down, whereas OSMC has more underneath it (it has apt-get for example, which LE doesn't) but can take a little more setting up sometimes.
In both cases I think they can be set up to automatically share any USB drives connected to them, which would perhaps cover your NAS needs if they are simple.
The other way is to set up a normal Raspbian Pi, and then follow the various tutorials available on the web for setting up a NAS onto it and also for setting up Kodi onto it. That has the advantage of being more flexible and general, but the disadvantage that of course it is not optimised for either and it can be much more complex to get running smoothly.
In the end it depends on how proficient you are with setting up such things, or conversely how much you want it "out of the box" and pre-built. But as all three are available for free, I'd suggest grabbing copies of them, burning them onto SD cards (or try each one by one on the same SD card if you prefer) and seeing which fits your needs best. Start with LE or OSMC and go from there, as they're the quickest and easiest.
Drive connection to the Pi would be via USB cable (there aren't really any other options for the Pi), and yes for a Pi3 I would certainly recommend some sort of case. The FLIRC case is highly recommended (especially the Kodi branded one
) as it gives the best cooling I know for a Pi3. Otherwise some sort of fan-assisted case would be needed, as the Pi3 (and to a slightly lesser extent the new Pi3B+) can run hot if you push it with high-def media and have thermal throttling issues. One thing to also make sure of is to get a decent 3A power supply. The official one from the Pi Foundation works very well for this application.
Another option of course is to split the workload up between two Pi's, and use a more dedicated solution for each. For the Kodi part I'd recommend LE or OSMC still, but if you want a more fully featured NAS-type solution something like OpenMediaVault works very well, and can support a lot of different protocols (SMB, NFS, FTP etc) plus via plug-ins cover things like Plex and VPN servers.
