Multiple possibilities here.
First, welcome to the forums.
Hopefully you will have already checked out the free User Guide and maybe some of the excellent video tutorials, all at reaper.fm.
This will make it a lot easier for you and us to figure out what is wrong.
It would really help us to help you if you told us WHAT audio you are recording (voice, instruments) and what you are using for an audio/MIDI interface.
If you are using a "proper" interface & it has ASIO drivers, make sure you have enabled it in your setup and have the ASIO buffer set to something sensible.
(Like I said, RTFM and WTFV.
)
Also, you may be using a plugin that is in demo mode, which often causes cut-outs or random white noise.