Painting In Your garage would be fine. Just know that it's probably going to be a dirty paint job compared to If you use the paint booth at your school. Which will probably result in quite a bit of wet sanding. I have a degree in collision repair and refinishing. My advice is ti use the booth if you can, you will be glad you did

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Also....I doubt you're gonna get a compressor for 150 that will sufficiently power a DA and a gun. I just bought a portable 33gal compressor for my DA and gun. It was $350. DAs use ALOT of air. My compressor barely cuts it and all I'm doing right now is putting some flares on my friends FC. I would hate to do a whole car with the compressor I have. Sanding wise i mean. It should power then gun just fine.
I would say get a 60 gal. That should work just fine. Also about the baking. You only need to bake clearcoat. Base dries quite fast. I learned with BASF Products (Limco,RM,Glasurit). Flash time between coAts with these paints is about 5 to 10 min. Baking the clearcoat is a great way to help it dry. But it's not always necessary. Keep us updated