Composting has become a fine art these days and most online composting 'fanatics' are tending towards a 3 bed compartmentalised method where you acquire a load of wooden pallets and position them, one pallet width apart. Ideally though, the top of the build should be covered either by a hinged lid or a tarpaulin.
The principle is that you put whatever you have to compost in the left hand side until it is full and let it compost down to about half the original. Since ideally it needs to be 'turned' at some point, you then turn it into the middle bay so it composts more, releasing the left hand bay for newer material. Effectively the middle bin will take all of the left hand bin twice over. In time,you then turn the middle bay and put it in the right hand bay wherein it is regarded as 'ready for use'.
This works well enough if you have incredible amounts of organic material needing composting but it is perfectly possible to scale this back to get smaller compartments or even reduce it down to 2.
Either way, it makes sense to keep the pile off any walls since it allows more air to get to the pile and since piles are moist to wet, they most certainly would begin to saturate your garage wall, leading to damp inside the garage.
The location you suggest however is ideal since it will be cool and damp and away from the sun and so, depending upon the volumes of organic material you will be adding you might also choose to opt for other alternatives.
The amount of composting I need in my garden is very low and my local council here in the UK have been selling recycled plastic dome type compost bins at a discount. In the big box stores they sell for about £35 ($45) but the council sold me two for just £10 each ($12). I now only ever put invasive weeds in my council organic waste collection wheelie-bin and put everything in the plastic dome affair. What I have however discovered is that it offers insufficient ventilation and I have drilled extra holes in the plastic to improve matters. And since it has a lid, I have to water it in with a few watering cans of rainwater occasionally. So far, 12 months into the trial, I have not yet seen adequate compost so I am not so far impressed. That said, I also have a few worm bins that are far more productive.
Another alternative would be to get a tumbling compost bin and whilst they have been demonstrated to be very efficient in producing compost marginally faster there is a cost of buying the device and also having to turn the drum regularly.
Bear in mind that whatever you do, the compost heap will provide you with an excellent source of decomposed organic material almost free of cost for the next season, though some hard work will be needed to ensure whatever system you choose performs to expectations.
You have to consider also that there is a risk of attracting vermin, though they are routinely present in all areas of a large garden anyway and a well designed composting system can always to build in some deterrent factors.