3/8" is good. The gaskets will compress a little when it's all bolted together.
If you're doing this with the engine in the car, I would get about 4-6 5/16" studs and place them strategically around the pan rail. Glue your gaskets on with Right Stuff or your favorite gasket sealer. Smear a thin layer in between each part of the sandwich to seal. Don't lay beads, as beads will find their way into the crankcase.
On the gasket that goes on closest to the block, look at the rear main cap and make sure the gasket doesn't cover the rear main seal drain. If it does, it could help the chance of a rear main seal leak. Take an X-Acto knife or razor blade and cut out around it. Also, if you're using ARP main studs (and some main bolts), make sure that they don't stick down below the cap far enough to keep the
oil pan from sitting against the block. Make sure the windage tray doesn't block the drain or hit on any fasteners as well.
Let everything seal up over night and don't put any
oil in it until you're confident it's sealed and dry.