This is a common question. To trigger a relay, even 22 gage can do this. The wire going to load has to be rated for the working amps needed, and the relay needs to be rated/designed for the task assigned. Seems simple enough, but you'll start getting advice from folks that googled it, having never built anything.
I'm not an LS swap person. Have a friend that is but not me at present. I build street and show, some resto mod 70 and 80s mostly, plus a few movie cars, remake on RobCop Taurus, and the old school ProStreet that few do anymore, plus do my own looms and last one was a 34 Coupe with a flat head.
On fans I go big, probably over kill but if I can go 30 amp and split it, I wont. I'll put a 30 amp on each fans. Relays that are designed to turn on and stay on are the ones you want. This is also true for fuel pump and electric choke.
The fuel pump needs to be powered through an oil pressure switch. You can use a relay or hard wire, but for safety it needs to run through an OP switch.
I E : The engine shuts off, oil pressure drops, fuel shuts off. This is very important in a crash where sparking can occur. Especially on off road or any emergency vehicles that have a master switch.
As far a conduits, I just use wire loom material. Comes in rolls, and diameters from 1/4 inch to 1 inch typical. There are plastic and metal clamps good for securing the loom. Keeps things neat and tidy.
You can go black, keeps it subdued and not very noticable, or use color for contrast and give a professional organized look. I like Blue and Red.
Dark color car like brown or dark maroon I use blue. Light color car like white or yellow I use red.