Conduit is your friend
Conduit is cheap, trenching is expensive, and putting fat conduit in now can save you more trenching later if your wires prove too small, as well as shielding the wire from mild cases of excavation damage which'd otherwise force you to dig up the cable and replace it. So, I'd put fat (2"+) schedule 80 PVC in the ground now, using prefab wide radius sweeps for the horizontal to vertical transitions.
Fat aluminum is also your friend
All the bad things that you may have heard about aluminum building-wire do not apply to what you are doing right now. The terminations you're working with (pressure setscrew lugs) are much better at handling aluminum wire than the wrap-type terminal screws or backstabs on receptacles and switches, the aluminum wire that you buy now is made from a different alloy with better properties for building wiring than the aluminum wire that gave aluminum its bad rap, and the busbars and lugs themselves on your breakers and panels are likely made from plated aluminum, too.
So, that said, I'd use 2AWG, wet-location-rated (THWN or XHHW-2) aluminum wire for both hots and the neutral with an 8AWG or 6AWG (8AWG works, 6AWG might be more useful for grounding electrode conductors though) bare copper ground wire. That will give you 70A at the garage without coming close to filling a 2" conduit.
Big (slots-wise) subpanels are your friend, too
Furthermore, you'll need a subpanel at the garage for this, and again, it's penny-wise and pound-foolish to skimp now due to the labor costs of redoing things down the road. I'd at a bare minimum put a small 20 or 24 slot, 100A panel in as the garage subpanel -- if you can afford something with more slots in it, do so, as often you can get kits with the panel, a main breaker, and some 15 and 20A branch breakers. Don't worry about the ampacity of the main breaker in the subpanel, by the way, as it's only serving as a disconnect -- the 70A feeder breaker in the main panel provides the overcurrent protection.
Last but not least
You'll want to use an inch-pound torque wrench or torque screwdriver (depending on the specified torque) to torque all the breaker and panel lugs to specification when doing this -- the 2017 NEC actually requires the use of calibrated torque tools in 110.14(D), and it's a good idea in any case to make a reliable connection, especially on aluminum wires.