We don't generally worry about upsizing 240V wire until about 180', so 10 AWG will be fine.
You only need 2 hots + ground. If you use cable, consider using /3 (2 hots + neutral + ground). That's for 2 reasons: it's round; and it improves ability to reuse the wiring for other purposes later.
You can use any of the following wiring methods:
- THWN/THHN wire in conduit - you might as well use stranded wire, which will be an easy pull
- Cable in physically protected locations e.g. inside walls
- Cable inside conduit provided the conduit is large enough
By "large enough" conduit, I mean the conduit's actual inside diameter must be 138% of the cable's widest width (hence the importance of round cable). However pulling any cable through conduit is quite hard, and upsizing just to make the pull easier helps a lot. A novice DIYer can easily wind up in a situation where you run out of swear words, and have to call in a professional :)
Anywhere you transition between THHN and cable, that must happen in a junction box. I recommend a 4x4 metal junction box so you have enough cubic inches. If you plan to ever use that conduit for other circuits, use THHN - multiple cables requires a HUGE conduit.