Good question. It comes up a LOT. I had the same question myself when I started. Check throught the archives for more info.
I'll recap what I think I know (others please chime in):
Propane is VERY explosive if it leaks, so don't cut corners. Don't risk it.
Eliminate all extra shut-offs, T's, and flexible connections inside the trailer.
All propane lines need to be routed outside (underneath) the trailer, and penetrate through the floor directly to the appliance.
The main line (vintage trailers, at least) are 5/8" or 1/2" from the LP tank regulator. The secondary lines branching out are 3/8".
Install the petcock shut-off's underneath, at the main line or where they penetrate the undercarriage.
Type "K" is thick walled copper pipe, listed for propane. Lowes and Home Depot usually don't carry it. They only carry "L" or "M" for water and refrigeration.
Use only flared fittings, so you'll need to purchase a flaring tool.
Too much argument about single-flared or double-flared due to code changes. Take it for what it's worth.
What I did (which may or may not be the "best" way) was redo all the propane lines that were crushed/damaged under the trailer, keeping the usable parts. I disconnected the branch lines, and installed new brass petcocks and double-end female swivle fittings at the existing "T". I routed new copper tubing to each appliance, and poked them up through the floor, using black rubber pipe at the penetration to protect the copper tubing. Inside I routed the copper tube directly to each appliance, and connected with a flared fitting. NO FLEX HOSE!
Underneath I also used a clear, braided hose, with wire ties, split along the length and wrapped along the copper tube, for extra protection. Also use the rubber grommeted clamps, to prevent chafing the tubes.
Here's a couple pics of what I did: