If you want to talk real serious power distribution, the proper way: use wire sized for the transformer (which I presume is fused too; usually on the primary side), run that over to a distribution block / panel, and connect individually fused feeders (smaller wire, fused for the ampacity) to it. Which, in turn, do the same if they feed smaller circuits, and so on.
The big hazard to keep in mind is, suppose a couple of those feeder wires get crossed or shorted, and they start heating up, but it's not enough current draw to blow the main transformer fuse, and foof, there goes a fire.
The North American standard is, every circuit terminates in only one or a few possible loads (lights, outlets..). The British standard is, you have a somewhat generous circuit that spans many possible loads (maybe one circuit spanning all the outlets in one or several rooms) -- with the catch that, each load is individually fused (they require line cords with fused plugs).
Of course, those rules exist because mains power has more than enough current and voltage to melt wires, ignite sparks, etc. Not nearly as big a deal at this voltage, but the available power is still probably enough to pay a little mind, especially if you have a *lot* of wire to run.
Fusing every little wire is probably a tedious pain, so you don't have to go that far. But it's still worth keeping that model in mind, so you can design a safe distribution network.
Barrier strips, or Eurostyle terminal strips, or DIN rail clip-on types (commonly used for industrial machines), are all very popular and effective. At the low voltage, insulation, isolation and protection aren't really a big deal (it's not like you need the fully shrouded 480VAC arc-flash prevention kind), but preventing shorts due to careless screwdrivers and stuff like that would be a convenience.
More tips to draw from industry -- use cable clips, cable trays or raceways to organize wires, or at least keep the mess out of the way. Panel wiring can be pretty great, you might image search some keywords for ideas.
Tim