Being in CA, you can have a 14.5 inch barrel with a properly pinned and welded muzzle device that gives your barrel an OAL of 16". For more info on this I'd suggest joining and reading the calguns.net message board. Also being in CA you can not own a suppressor unless you are a FFL 07/02 SOT as far as I know, you could check with OC Armory in CA, they sell suppressors to people outside of CA and to LE.

As for the 'thick" barrels they are called a variety of things, including "heavy" and "bull." Often you will see "Match" barrels with this look as well. I'm sure others on the board can give you more information on this, but I'd suggest taking these questions to calguns.net since you are in CA and our state gun laws are very different than the rest of the country.