Sub panel for garage
Sure you can, the size wire will be based on your load. I would put in 2 or 4x what you think you need to start with because as soon as you get it done you will find something else you want then in 5 years a electric car charger , I have never reduced the size of a service but many times gone back and increased the service in 1 case we did it 3 times , a few lights and outlets a 30amp 240 v feed would be fine but get a 100 amp main breaker panel and put in at least 1” conduit now you can run #10 thhn/thwn wires wire to the panel and in the future if you need larger you can go all the way up to #4. You put a 30 amp double pole breaker in the main panel and your sub panel is set up for future possible growth. A garage or out building all the outlets need to have GFCI protection even the ceiling receptacles, if the lights are direct wire they don’t require GFCI protection. You will also need a ground rod with #6 copper going to the ground buss and the Neutral buss needs to be isolated from ground in a sub panel (they are connected in the main only). Hope that helps. FYI your voltage drop at a full 30 amp load would be 2.62% the max recommended is 3% so you are good there, if you can afford larger wire go as big as you can, I purchase wire online much of the time and one place to get a good deal is wireandcableyourway.com no association other than having purchased thousands of feet, best price but takes a few days.

Always purchase more than what you measure if your total length is 112’ panel to panel order 117’ it is better to waste a couple of feet than be an inch short and even measuring with mule tape that is marked every foot I find I always need at least a foot or 2 more than the measurement was , my apprentice just learned this lesson on a 150’ pull he ordered the wire pre cut at 154 and we ended having to splice lucky we were inside a machine center and could splice or we would had to put a junction box in and splice there wasting more wire as the breaker was at floor level and the conduit was in the ceiling he now has no problem wasting a few feet.