Trenching and running power to detached garage about 135 feet away
You need THWN

Since underground conduit is assumed to be full of water, you need wet-location wire, such as THWN.  Fortunately, garden-variety building wire you get for conduit jobs is dual-rated THHN/THWN 99.9% of the time, so finding THWN is just as easy as finding THHN.

Also, use a bare copper ground wire -- you'll need to use 6AWG for this if you use the 6AWG copper or 4AWG aluminum hot wires because of 250.122(B) which requires the ground to be upsized when upsizing wires to control for voltage drop, but you'll still be able to save on conduit fill area that way.  The phase and neutral wires can be copper or aluminum as they're running from breaker lug to breaker lug most likely anyway, and breaker lugs have no trouble with aluminum wire provided they're torqued correctly.

Put in the fattest conduit you can get

This is a job for the fattest schedule 80 PVC you can lay your hands on -- it'll make future upgrades easier, and also make your pulling job easier especially since you have 135' and two 90deg sweeps to contend with.  Also, make sure to get Schedule 80 -- it's more resistant to accidents than Schedule 40 is, which is important for the terminations.

You'll need a disconnect at the garage (and perhaps a ground rod too)

You'll need some sort of disconnecting means at the garage.  A spa disconnect that's been retrofitted for straight-up 120V use works, or you can even use a 20A light switch, but the best plan is to put a decent sized main breaker subpanel in a NEMA 3R enclosure in there (a 20 slot, 100 or 125A unit with a backfed 20A main breaker would be my bare minimum), making sure the bonding screw gets pulled (unless you go with Harper's transformer plan) and the neutral and ground feeder wires are landed to the correct busses in the subpanel.  This does mean you'll need to run some more of that bare 6AWG copper from the subpanel grounding bus to a driven ground rod as the exception to 250.32(A) no longer applies, but that's cheap (and good) insurance even on an underground run (I'd consider it mandatory for an overhead run).

Last but not least: TORQUE MATTERS.

One thing you'll want to make sure of with this job is that your connections are torqued to manufacturer specifications.  "Gudntite" can easily be too tight, leading to connection failures down the road with setscrew lugs, especially with aluminum wire as it's softer and easier to damage than the stiffer copper stuff.  Also, this is a requirement as of the 2017 NEC, see 110.14(D) for details.

In practice, this means you'll need an inch-pound torque screwdriver for torquing down the connections properly -- make sure it can go down to 10 in-lbs for receptacles and switches, and up to 50 in-lbs for torquing down the breaker and lug setscrews.  Better that than the electrical version of being Greg Biffle trying to lose lugnuts mid-race, don't you think?