Run electric from breaker box in house 150 feet to garage, only need 110, 10 receptacles and 6 lights
As for wire size, you did not say what loads you want to run.  Here is a calculator tool - enter your cable run (150ft) not the round trip (300ft).  The breaker in your main panel is sized to protect that wire.   Think about upsizing - wire or conduit is cheap, labor and digging are not.  

If direct burial, USE-2 or UF.  If in conduit, THWN single-wire.   Price the various wires but you may be better off in conduit and pulling just the size of THWN that you need.  Lay extra large conduit so the next guy can pull bigger wire if he wants to. 

You must use correct colors of THWN wire.  White or gray for neutral,  green or bare for ground,  anything else for hot.  No remarking allowed, except mark all you like on #4 or larger wire.   

Aside from what Tyson suggests, a good reason to have a sub-panel is so your lights are on a different circuit than your tools.  Nothing is worse than tripping the breaker and plunging into darkness with your fingers 2” from a spinning blade.  Also, outlets cannot have larger than a 20A breaker, so if you ever want to provision more than 20A of service out there, e.g. For a dust collector, you'll want a second circuit and therefore a sub-panel. Demand can sneak up on you.  

On the sub-panel, price several larger sizes and get the one with the most spaces that you can bear.  No homeowner ever said "I have too many spaces in this panel".  Its OK to run a 60A or 125A sub-panel on a 30A breaker in the main panel. 

If you want to run 120V only, just do the sub-panel in the normal way and don't hook up one of the hots. Every other breaker row will be dead.  Who cares, just don't put breakers there.