Free Speed is the speed of the motor output shaft at max power with no load. This is important to consider for gearbox pairing, If you have a high speed motor and need high speed, then you will not need much reduction. If you have a high speed motor and need high torque, you will need more reduction. Free Speed is usually measured in RPM (rotations per minute).
The most power the motor will use in watts. This is important to consider for motor application and breaker placement.
Torque put out by the motor at stall (with the output shaft locked). This is important to consider for high-torque applications such as drivetrains or climbers.
Thermal Mass / Cooling
The reason CIM motors are so popular for drivetrains is because they have high torque and very high thermal mass. Having a high thermal mass means the motor can sustain a stall (and just rapid acceleration/deceleration) for a longer amount of time without overheating. It's also important to consider that some motors such as 775 Pros are actively cooled with a fan on the output shaft and have a low thermal mass, which means they will burn out very quickly if stalled at high power. If you're using a 775 Pro/Redline for an elevator, you might want to use constant force springs, or just have enough friction in your elevator so that it can hold itself up without stalling the motors.
CIM and Mini CIM
CIM and Mini CIM motors are the bread and butter of FRC. They've been around for forever, and you're bound to find a bunch laying around the shop. They are relatively slow (still fast enough for almost all applications), but very torque-y and reliable brushed motors. They have a very high thermal mass and don't rely on active cooling which means they can be stalled for a very long time without being damaged. Generally, CIM motors have been replaced by NEOs, which weigh almost 2lbs less and produce even more torque. CIM motors are controlled with Talon SRX or Victor SPX motor controllers.
NEOs are some of the best motors available right now and are great for many applications. They are only slightly heavier and bigger than a 775 (0.1lbs), and can produce almost 4 times the stall torque. They have a fairly low free speed (about the same as a CIM), but can be geared for higher speeds. If it makes sense to use a CIM somewhere, it probably makes more sense to use a NEO. NEOs are brushless so they have 3 leads and are controlled with a SPARK MAX motor controller. NEOs also have built-in hall sensors which means encoders aren't needed for most applications. The hall sensor has a resolution of 42 counts per revolution, which comes out to about 9deg of resolution before any reduction. Consider that if you use a NEO, you might not need to deal with encoders in your design. The light weight, small size, high torque, and built-in encoder make NEOs fantastic choices for almost any application.
775 Pro / Redline
775 is a size of brushed DC motor. Two common 775 motors in FRC are 775 Pros from VEX/WCP, and Redlines from Andymark. They are basically the same motor. These motors provide the best power/weight and power/size ratio of any brushed motor. These motors have an extremely high RPM and do not like to be stalled since they're actively cooled by an inner fan. When the fan can't rotate because the shaft isn't rotating, these motor will burn out very quickly. These could be used for an elevator, but a CIM or NEO might be a better choice, since elevators (without constant force springs or lots of friction) need to stall to hold the elevator up against gravity. They could also be used in a drivetrain, but again, for high torque applications a CIM or NEO might be better. These motors are very good for things like gamepiece manipulation (intakes/outtakes), flywheels, shooters, etc. These motors are controlled with Talon SRX or Victor SPX motor controllers.