I have two 120V 20A circuits to my Rion 8x12. Run a 1500/1750W space heater off each circuit, plus misc. stuff like fans, a light, propagation mats... This is to maintain 58ºF when our night temps occasionally get into the teens. I already had one circuit out there serving another gh when I erected the Rion, so being lazy, instead of running a single 240v 20A circuit to the gh, I just ran a second 120V circuit. If I were starting from scratch, I would run a 240V 20A circuit to a small gh.

This post is very timely for me. I am today finishing my trench to be used for the run of electrical (and also use for my water line) to the gh. I am running the line in a trench from my well which has 240. At the well, I intend to install another box next to the well box, connect to the power there, and use 3/4" elec pvc sched 80 to the gh - about 40'away, using #10 wire. The new box is a 30AMP box with two fused circuits and I am going to use two 20amp fuses. I was only going to run one 20amp line to the gh, but then thought I might as well put in another wire so I will be able to have two separate circuits in the gh. Gh is 12x11, and given my zone etc, I can get by with one heater, which I anticipate won't be needed very often. Other uses of electrical would be exhaust fans and shutters, circulating fan, lights, and any power tools I might need to use from time to time.
I do not know if this is the optimal way to proceed, but I think it will work out for me.

I'm only a "shade tree" electrician, so for what it's worth: Be sure to use UF cable underground. Supposedly, UF can be direct buried without encasing it, but I would still encase it in pvc to help protect it from spades, tillers, rodents etc.

Billala, thanks. I intend to use wire enclosed in schedule 80 electrical pvc pipes for the entire length - the wire will not be UF cable, just the wires - Red, Black, White, Green. Per code, I will have it in excess of 2' down and will bury it with about 6" of dirt and then lay a run of yellow caution ribbon, then another foot of dirt and then another run of yellow ribbon.

brandond: NOT 2-wire: 3-wire only. The cost difference, if any, is very little and far less than a funeral. Then add a copper ground post and install only GFIC outlets, as high above where you expect to be spraying water as you can comfortably reach.

Water and electricity can be a deadly combination but as you will using both in your GH, don't skimp on the materials used to install the one that can be your servant- or executioner.

Go with 20 amp. and while you are at it, add an extra circuit. It may go unused, with little waste of time and materials, or very likely sometime in the future you will be grateful to have it. Never underestimate the number of electrical gadgets you may eventually want to use in your GH and having an extra circuit to tap into will allow you to do so without overloading the others.

As the wise man once said: "To pull a rabbit from a hat, first requires there to be a rabbit in it."

Absolutely, as birdwidow states, you need three wires - one being for grounding. The Romex type wire will be designated as 12/2 wG, meaning 2 number 12 wires and a grounding wire. 12/3 wG would be three number 12 wires plus a ground. If you are going underground without a conduit, you need a special Romex type cable suitable for underground and need to go deep, I believe at least 24".
As suggested, if you want two circuits, you will need a 12/3 wG, (you need that third wire plus a ground) and if your run is long, you may want a larger wire, e.g., #10.
If you go with a conduit, you should not use Romex type cable in the conduit but need to pull separate wires of the appropriate size.
As Birdwidow states, be very careful, use GFI fixtures, and if this is something you are unsure you can manage, get help.