Assuming there's anything worth having in the garage (including tools to burglarise your house) I'd fit a 5-lever BS 3621 lock with 5 brass levers.
I always use Chubb and have all the locks at the back of mu house suited to the same key, but you can get quite good BS locks by Legge for less, and i saw some own-brand BS locks at
Screwfix as well as Homebase which I expect are OK.
The BS does durability as well as thief-resistance so you should be OK with any make. Measure the old lock, the new one will probably be the same size (different makes vary by a few mm) but a bit thicker so you will need to shave the lock mortice with a broad chisel so its an easy sliding fit. it will also have a very much stronger staple (the bit that goes in the frame) so you'll need to chisel this out neatly too.
What method did you use to remove the old lock?
Put on a keyhole with a swinging cover to keep the weather out, and preferably on the inside of the door as well - it'll reduce drafts carrying dirt and grit into the lock.
BTW, big (car size) garage doors are not very secure, you might think about adding a few big steel bolts to the top and bottom to make it difficult to force, you can operate them from inside, and use the personal door at the back as your final exit.
Incidentally, you can often buy Chubb locks on Ebay at a good price, perhaps where someone has bought the wrong size. If buying by post have it sent to a friends house, you don't want anyone who might have a spare key knowing the correct address.