Where do you live and shoot? A long range cartridge is not appropriate if you are lucky to even have 100 yd open areas.
Whatever you do, just make sure that you build it as a "handgun" initially so that you can convert the lower between handgun and rifle and back as you see fit.
My first one was a 5.56 and the second one was a .300 AAC. The .300 AAC has about the ballistics of a .30-30, so it might be an acceptable deer gun. There's been plenty of threads debating this on this site and others. Have fun reading through all of them.