If you are going with 120v, the current in the power wire is the same as the current in the neutral, so use the same wire, 12g, for each. I've seen ground wire on some old romex wire to be a smaller guage, which I thought wasn't safe. Say 12-2 with ground, ground may be a 14g. Today, all three wires are the same, 12 guage.
Yes, I've run stranded and solid in conduit when running wires underground.
Let's look at the math. $1.59/10 ft. 100 ft is $15.90. 200 ft is $31.80 plus glue, plus fittings. What's the price of 250 ft of 12-2 with ground? If you only have 500 ft, you will need to buy 200 ft of wire for your third wire. SO WHERE IS THE SAVINGS? It can't be that much and I would find no joy pulling 200 ft through conduit.