Spiders won't actually hurt anything, mice rats and squirrels will eat plastic/rubber and fill cavities with nests and food caches.
Put out poison for the rodents. Squirrels are cute I suppose but don't belong in any garage, mice and rats are just plain vermin. Look for where they get in and plug any holes. Mice are going to get in any garage, they fit under very small gaps, but squirrels need a good sized hole.
If the garage is not occupied much (like you don't have poker games in there for hours) especially with the door shut, get Vapona no-pest strips. These gas off insecticide and kill any bugs that spend a lot of time in there. A good blasting with a can of Raid to clear out the place is good first though - close the big door almost all the way so you can get out underneath or all the way if there's a small door, take a few deep breaths, and spray the whole dang can out towards the walls while holding your breath. Get out and close it up as tight as possible. After an hour or two go in and hang about double the recommended number of Vapona strips for the cubic area of the garage. Keep it closed as much as possible and spiders should not be a problem. The strips last about 2 or 3 months.
Take bikes and cars out before the Raid spraying, droplets might damage the paint.