If your main supply is not PME, consider at least 4mm 3 core SWA, and use one of the cores as earth,m in addition to the armour, which must be securely glanded at both ends.. At the house cover with 32A trip, and in the garage have small consumer unit, with RCD, 6A lighting breaker, and 16A breaker for a 2.5mm radial feed to a hand-full of sockets. If there is any risk of this not being enough for unknown future demand, then 6 or 10mm are the next largest options, and while probably overkill, some will recommend them as future proofing, depends if you are a power tool freak, and worried about the lights dimming a bit as you and yours use the plasma cutter and arc welding equipment together...
What I have recommended is for lights plus a l bar fire, and either a lawnmower or electric drill, but not both at once type of user.
If your supply is PME, you would be well advidsed to install a local earth spike at the garage, and only use the house earth to protect the cable armour on its way out there.
regards M.
PS If this is a new circuit, and all works started this year, then the dreaded part P bites, and strictly to stay within the new rules, you should notify the local building control office, who will charge to infect your work.
(or employ a sparks belonging to a self certification scheme at vast cost.)