Will I need to reinstall games - if you aren't changing the storage, you might not have to. However, what you will have to probably do is re-install Windows, so you definitely want to backup whatever important files are in your C: drive, because it's going to get formatted.
New RAM - first it's best you check if the older RAM works in the new motherboard, before ordering new RAM. If you are sure it isn't working, then yes, you'll need new RAM.
Motherboard suggestion - Asus Prime Z270-A. Good aesthetics, good build quality, good reviews, good Asus BIOS, and other bells and whistles you may need. Usually a good all-rounder, but there are many other options out there in case the white clashes with your build. If you want different aesthetics, the Asus Maximus IX Hero is excellent, MSI Z270 Gaming Pro Carbon is also good. There's still a lot of other good boards, but these are the ones generally considered good.