If you look at factory installed VFDs, they generally reduce the gearing/pulley ratio to 2 or 3 speeds, the rest of the speed range is handled by the motor. The motor is generally oversized by 1.5-2X so that the performance (Hp/Torque) is similar to the non-VFD multi-speed version. The goal is not to have a faster spindle speed, but to adjust the ratios for optimal performance over the desired spindle speed range, so you have a mechanical advantage when over speeding the motor and changing the drive ratios to give the same spindle speed as a 60 Hz. motor. So if you have a 2 Hp motor 60Hz with a 1:1 final drive ratio vs. a 2 Hp motor at 120 Hz with a 2:1 final drive ratio, you have a mechanical advantage of 2X with the latter with the same Hp. You need to change the drive ratio when using a VFD. When you go below the motors base speed the torque is flat and Hp drops in a linear fashion, but you loose the mechanical advantage if you are running the VFD at say 20 Hz instead of 60 Hz. In practice most VFDs can provide up to around 180% torque for up to 1 minute, beyond that you will get an over current fault if you exceed 100% of the output amperage.
TEFC, TENV and TEBC are pretty much the industry standard for motors on lathes and mills in the 2-5 Hp range, and larger. TENV and TEBC are primarily used in VFD driven motors. The cooling will be better at speed extremes due to the mass/design, and there is no risk of chips/swarf entering the motor with a totally enclosed case.
Regarding a brake resistor, there is usually a range of resistance specified by the manufacture based on the size and voltage of the VFD, and it is also dependent on the type of machinery being operated (momentum and frequency of braking) and if the braking is static or dynamic. I have attached the recommendations for the Hitachi WJ200. Bigger/lower resistance is not necessarily better, the lower the resistance the more voltage/current can be dissipated over a shorter period of time. This is at the expense of a decreased duty cycle, or frequency of stops over a given time period. Since in mills and lathes, there are not a lot of stop start cycles and there is no static brake hold, usually being at the lower end of the recommend resistance is preferable. So something like the 2 Hp 200V WJ200 I usually recommend something in the 50-75 Ohm range for a braking resistor. Since common resistor sizes are 47 Ohm and 68 Ohms, I recommend using the 68 Ohm. On the 3 Hp 200V WJ200 either 35 or 47 Ohm resistors are commonly available sizes. With high braking duty cycles the resistors can get very hot, and there is usually a thermal oveload contact built into the braking module provided by the VFD manufactures, in mills and lathes this is not needed because of the low duty cycle time.