You need to determine maximum torque required for continuous operation and the speeds at which the torque will be required. You need to determine the maximum intermittent torque required and the duration and speed for which it will be required. Then select a VFD and VFD-duty motor combination that will provide the required torque-speed performance. Worst case operating point is usually zero-speed starting torque and minimum continuous operating speed.
As a rule of thumb most 3 phase, 60 Hz, 4 pole, motor/vfd combos can produce very near continuous full torque from 400 rpm to 2000 rpm. This is called a 5:1 speed range or turn down ratio which is going to be some around 14 Hz to 68 Hz.
Many DC systems I have changed to AC had the DC motor running very slowly during operation so I had to change the gearing to keep the new AC motor in its preferred speed range.
If you need something more than a 5:1 speed range you may need to get a vector drive and vector duty motor. There is no set terminology for the capabilities of vector drives or vector motors so read the specifications.
As CJCPE said you have to know speed and torque. You cannot just go by horsepower.
As CJCPE has already hinted, pay particular attention to breakaway torque requirements - most DC drives have the capability to provide enormous torque at standstill if required by the load. Failing to consider it has tripped up quite a few people converting from DC to AC.
If the existing DC drive is a 4 quadrant drive, you will need to pay particular attention to the brakeing abilty of the AC Drive and motor. You may need to consider either a high brakeing torque dynamic brake resistor, or and active front end drive.
Many DC Applications that I get involved with, such as log shuttles or carriages, provide fast acceleration and deceleration in both directions.
