I used to play on Behemoth but a friend of mine, long story, ended up going over to Leviathan. I don't really want to spend the money to transfer a character, so what's the easiest way, if at all, to get my gold over there?

The easiest way if you can't find a very trusting person to trade with or get mediated, is to buy up all the stuff cheaper on the market board on your server, and transfer an inventory full of materia and mats etc. to the new server and sell it off the boards there. If you do the transfer normally you will only be able to keep 1 million actual gil.

You are 99% of the time going to have to suck it up and do the server transfer for 10 dollars or whatever it is.

It's 18, so I'm just going to let the character stay there

Nope

Check MB on server ur transferring to and stock up on stuff that sells high n well. U can usually make a profit outta it too