Tile over concrete?

Congratulations on  your <i>almost</i> completing the garage finishing project! You do still have an important piece left though and you are absolutely right in putting some additional research into this. I have seen it done both ways - just directly over concrete on modified thinset mortar as well as on a Schluter DITRA underlayment - and you can have satisfactory results without underlayment.

HOWEVER:

There are a couple of things to consider since this is a garage slab.

Garage slabs are often poured without moisture barrier over the fill because garage is considered an outside area and besides, you do bring enough water on your car driving in the rain or snow to not bother with moisture barrier. This means that the moisture does have a tendency to migrate through garage slabs more. You can actually do a simple test while you're looking for information and gathering materials. Cut a 3'x3' piece of poly plastic, preferably thicker like 3mil, lay it on garage floor and seal the edges with duct tape. Leave for 48 hours or more if you have time, then remove and look at the area which was under plastic for darkening of the concrete and any water droplets on the plastic or the floor or signs of salt left by water that's already evaporated.

You may find that despite having no visible cracks, there's still some amount of moisture on the slab, it's just hard to notice it, given that garage is not an air tight environment, and water easily evaporates. Now that you're finishing it, it will become an air tight environment and moisture dynamic is going to change.

Concrete may still develop cracks even though the hydration has almost been completed after 30 years and no considerable shrinkage will occur. But you're going to change the temperatures at the top of the slab now that this becomes a heated/air conditioned area whereas all its life it was exposed to temperatures close to the air outside.

Garage slabs are normally formed with a slope towards the door just so that water you bring on the car on a rainy day drains outward.  You may have 2-3" next to the door (progressively less as you move inside) you need to raise to plumb the floor level. Having an underalyment may help because you can mud the floor up as needed with dry pack mortar ( a stiff sand-cement mortar), then lay DITRA on it, level it, and then install the tiles on unmodified thinset over DITRA and level it once again, this time you can do it with fine precision.

I guess what I'm trying to say is that even though a good underlayment like DITRA (

) does add installation time and about $2 per square foot, it also addresses several issues specific to your situation. Besides, there's an important psychological factor  here, too. Fixing any potential cracking will be rather difficult once the project is complete. If anything at all happens, you'll be beating yourself over the fact that you did not do as much as you could to prevent the problem. And I don't really understand advice given on the condition "if you worry about cracks". Of course you should worry about cracks, in fact the best time to worry about them is now, when you can do something to prevent them. 

So, do the moisture test, look for a supplier (and a couple of alternative ones) of good underlayment to have a better idea about the actual cost increase and then make a fully informed decision.