Baris,
Well, we've done our duty and at least warned you of the limitations.
Re: AC Var frequency drives: Baldor would be one choice. Note: if you will be running this machine from a single phase power source, you can pick an oversize drive (by hp rating), and get three phase out of it. I am assuming the machine would be equipped with 3 phase electrics. At any rate, you must use a 3 phase motor with a variable frequency drive.
Baldor makes both Vector and Vectorless drives. What this amounts to is the method of providing motor feedback: Vector is likely out of your budget, because it requires a spindle encoder for feedback. This style of drive gives much better torque and accurate, consistent speed.
The other type, the Vectorless drive, uses some kind of internal logic to estimate the speed and load, and tries to maintain it. Low speed torque is not good on these drives. Likely they are intended for applications like HVAC where the maximum range of motor speed would be within 50% of rated motor rpm. I've used both types on mills, and the only place where I've had trouble is tapping with a Vectorless drive. The results of the spindle speed command is a crude guess at best, and this makes it difficult to guess the feedrate for threading. Plus, the torque is simply missing for low rpms.
You simply need to make the choice about which type of drive you intend to use, and tell the salesman about your motor hp and description of your input power source (single or 3 phase).