Wire gauge needed depends on distance and amps pulled across it. You want an AWG chart. Found all over the net 
Oversized buss wire is o.k. and can be safer too. Look for soft wire too; some insulation is very stiff and a PITA if it needs to bend. The stiff stuff is great for runs, but not so much for pig tailing (drops, accessory power, etc.)
(You can use multiple wires to equal a larger wire, yes.)
Fuse or breaker(I just say "fuse"; from work lingo... they do the same job) outside the transformer; before the run(s). Wire size determines max fuse amps that are safe to use. (If the wire is big enough to handle all the transformer power at once, then you can almost skip fusing again. Fuses at that point would be at, and for protection of the individual things you run)
Transformer breakers are not designed to save the track and trains; they save the transformer. (they afford some protection to track, but it's not ideal and coincidence)
