Last I played with the SEALs (90s) they were primarily using the MP5 (N & SD2), SIG P-226s, S&W 66 (for ops in silty water), silenced Ruger Mark II, and pistol grip 870s.
In reality they could carry anything they wanted. I saw folding stock M-14s, Browning Hi-Powers, Glocks of all flavors...