Air compressors are actually fairly complex units when you start to look into the finer details.
Things to consider:
Type of compressor. Most common style for small users is a reciprocating piston comp, but in industry rotary screw compressors are king. Small scroll compressors also exist, which are usually lower output in pressure/volume, but make up for it with quiet operation. If you need intermittent air at lower volumes, a piston compressor is usually the play. LOTS of air or air at a very steady stream? Rotary screw is the way to go.
Type of lubrication. Less expensive piston drives use splash lubrication, which is usually sufficient, but not as reliable under more heavy duty use. The connecting rods literally have little dipper arms on them that dip into the oil sump and splash the oil into the places it's needed. A pressure lubricated compressor uses an oil pump like your car's engine to pump oil where it is needed. This is usually considered to be the more reliable and long lived option, but at greater expense.
HP of motor driving the pump. Most of the time this scales with pressure and volume, but a home shop can run just fine on 5 HP. The more important thing to look at is the RPM of the motor, and the phase of the motor. 3 phase motors are preferred, but you will need a VFD to start one if you don't have 3 phase. This is nice because you can soft start/ramp the compressor up so you don't pop a breaker or can use a smaller breaker than a single phase would normally need due to the inrush current. Cheap compressors typically use higher RPM motors to spin the pump faster to get more air out of a smaller setup. This wears them out faster and makes more noise. Higher quality compressors will typically run a larger pump at a slower speed to produce the same air. This is not a hard and fast rule, as some are obviously designed for running faster or what have you, but in general, slower speeds on bigger pistons is preferred.
CFM and pressure of pump. This is the most important part of the air compressor. You typically want the highest volume you can afford. A single stage compressor will push out a lot of volume at around 120 psi. If you need pressure, that will usually come at the expense of volume. This is achieved by compressing the air a second time in a second stage, thus for a given HP you get either higher volume or higher pressure. Most tools and uses want VOLUME not pressure, so a two stage compressor isn't always the big win you would think it is. Most air tools are designed to work at 90 psi. That isn't 90 psi static, that is 90 psi in operation. When you pull the trigger on a die grinder, you'll have a pressure drop. What you really want is a compressor that will feed that tool at 90 psi IN USE while the tool is working. If you set your linework to 95 psi, you probably will only see 60-70 at the tool.
Volume of receiver. This is tied to the pump type. A single stage pump will usually want a LARGE receiver, as it isn't packing as much air into the tank. A two stage pump can pack a lot more air into a given tank size, but it will do it slower. I don't think you would want to go less than 50 gallons, personally speaking.
Type of receiver. Vertical or horizontal are your two choices. Horizontal has it's benefits, primarily when you get in the bigger capacity. Vertical is usually better for smaller spaces as it takes up less square footage. They also drain easier and rig easier.
Duty cycle. How much will your compressor run before it overheats? If you're just using a rattle wrench and the occasional spray gun, this probably doesn't matter. But if you're getting into sandblasting, you can EASILY outrun most compressors. I used to rent a tow behind screw just to blast with because a pressure pot blaster uses so much air. Same with the big power hammers in the blacksmith shop.
At the end of the day, most any compressor will work in a home shop. The true test is in industry, so you won't push anything you buy to the breaking point in your garage.
That said, I would personally buy a pressure lubricated Quincy, Saylor-Beall or Ingersoll Rand for my home shop. 5 HP is plenty. I'd get a vertical tank, 50-80 gallons with a timer on the drain. I'd use an air dryer. I would use a 3 phase motor with a soft start VFD. And I would run 3/4" or 1" main lines to my drops, black iron pipe, with moisture drains at each drop.
For my industrial shop, I have a 10HP Atlas Copco screw compressor, and you'll never convince me to go back to a piston drive in a pro setting due to the astronomical difference in noise and air volume per HP the screw provides. I gave my dad my 5 HP Quincy configured like I described above and he uses it in his home shop very happily.
