I have tried to use a hi/low configuration on VFDs using two speed motors, but my tries to wire the VFD to operate/use both speeds has been lack luster and often with disappointing results. This includes programming the VFD for both motor settings, which many VFDs include in their setup. My experience is to wire the motor for the low speed motor setting and directly wire this to the VFD. The motor connections should be clearly marked on the motor/connection cover. There are some exceptions, I have not dealt with 2 speed constant Hp motors in VFD conversions. You can comfortable over 1750 RPM speed (4P) motor to 1.5X it base speed of 60 Hz. Two pole motors (3450 RPM) usually are limited to 1.25X their base speed, I usually do not over speed them. You could push a 1750 RPM motor to 2X its base speed, but unless it is an inverter motor, there are some performance drop offs. Since high speeds are usually associated with smaller end mills/drills, you probably will never notice the difference and this is what I would recommend. Since the motor was already designed for this speed, cooling and bearings should not be an issue. You also gain motor performance by over speeding because of the ratio of motor speed to spindle speed. Torque wise, a 2P motor spins twice as fast but had 1/2 the torque of a 4 pole. When you add it all up with gearing/drive ratio to get the same spindle speed, I think it is a wash on torque. Still, in my experience you get better motor performance using a higher number of motor poles using a VFD. Granted this is empiric observation from a number of installation.
VFD wise recommendations, well it all depends on your budget and application. I would say 80% of the VFD builds/installs I have done have used the Hitachi WJ200, and it works well and has been reliable. Kind of middle of the road. Teco VFDs comes in many flavors and models, I would recommend a Teco (or most any other VFD) over an HY for numerous reasons. The HY may be more "economical" for especially for larger "single phase" input applications in the 3+ to 10Hp, but reviews and from other forums and VFD gurus really question both the build quality and the stated claims. It is the only VFD that I have heard of routine failures, so hit or miss, at a price point. Cheap it is works, Automation Direct has commendable VFDs, and their manuals and Tech support is great, but their VFD models are becoming dated, so like their popular GS2 model does not run sensorless vector control (I would go with the GS3), which provides significantly better motor control at lower speeds, and the GS2 is somewhat limited in the programming department. Still, on a mill it is more run forward, stop, run backward commands and a speed pot. Many people over think VFDs and the myriad of programmable parameters, when it comes down to it, in most hobbyist application there are only a few parameters to set to get your machine running. Many/most of the parameters are for much more complex applications. Yaskawa makes very nice drives, along with ABB, and a few other higher tier manufactures. In this application, I can't say that you would see any difference. Since I tend to design a bit more complex VFD systems with "more features" I use drives with more programming flexibility and inputs.
There are a number of posts regarding installation of a VFD on mills, wire the VFD directly to the motor, wire the VFD input to power via a disconnect preferable using a breaker or quick acting fusing. Use a remote pod for a speed pot, E-Stop, and run controls. The run commands/controls can be 2 wire control using a Forward Off Reverse switch just closing the input contact, or 3 wire control with momentary Stop, Run and motor direction. With 3 wire control that uses momentary controls, in most case will not auto start if power is applied vs. 2 wire. Most VFDs also provide a setting so the VFD will not run if powered up in a run commend mode. This does work, I have tried it on several VFDs. So some basic skills, but a VFD on a mill works very well in most applications, usually stepped pulley drives are preferable to the mechanical varispeeds.