Paul's right, a VFD is nice. I just bought one from Dealers Electric,
http://www.dealerselectric.com/, stock #T202, a Teco FM100-202-N1 for $246.00, new, in the box. It'll run up to 2 HP on single phase 220 VAC and would work good for your setup. I'm using it to run a 2hp bridgeport and converted my lathe to 3/4hp 3 phase from 1 hp single phase (runs much smoother). I simply used 3 three way switches (one on each leg from VFD, only switch with power off!) to switch between the 2. I don't use both at the same time. I already had a home made rotary (idler and small single phase for starting) for a 5 hp air compressor, but it was so much simpler installing the VFD instead of running wire all the way across garage, balancing it with caps and relays and so forth to make it automatic. The rotary is 7hp and pulls 11 Amps just running plus the AC motor another 9 or so. The VFD pulls about 2.5 A total so far (rated 7.5 A max) and is much quieter, plus variable speed for the lathe. My "rotary" ran at 3400 rpm and the cooling fan made it sound like a turbine. If your planning on running both machines at the same time, I am not sure about using the VFD.
One thing to think about with VFDs though. You don't want to switch the power between the VFD and the motor. You use the VFD for your forward/reverse/stop functions. You either use the VFD panel itself, or make up remote switch panels, which is what I did. I wired the VFD to the main contacts on the machines, but leave the original machine switches in the Forward/On positions all the time.
To specifically answer your question though, I would think a rotary is better. (My understanding is) Statics are basically the same as a capacitor start on a single phase motor. Once the motor starts, the cap cuts out and the motor continues to run on only single phase 220, so you don't get the full rated hp. With a rotary, your getting a third leg, so it's closer to true 3 phase.
If your making your own rotary, here's a quick and dirty that I used for years. Get a 2 or 3 hp three phase motor, RPM doesn't matter. 2 hp should work, 3 hp would be well on the safe side for your case. Take a 1/3 or 1/2 hp or so single phase motor and clamp to the SINLGE phase motor a piece of heater hose that fits snuggly on the 3 phase motor shaft. I had a simple plug cord on the single phase motor, the three phase had a hard wired cut off switch. I had the 2 motors on the floor facing each other. With EVERYTHING off, I slid the single phase motor over until the heater hose slipped over the 3 phase shaft and gripped the shaft enough to spin it. Plug in single phase motor. Motor starts, heater hose sqeals a little until 3 phase spinning at same speed. Turn on 220 single phase to 3 phase motor, motor runs, slide single phase motor back to disengage heater hose, unplug motor. You now have 3 phase to machines. Very unelegant, but worked fine. My 3 phase motor was 3400 rpm and the single only 1750, hose squealed when you turned on power, just reminded me to unplug and slide back single phase motor. Even with 3 ph motor not spinning at full speed when I applied power, it never failed to start. I ran a 5 hp air compressor for years on this and even used it for the mill when I first got it and it was sitting near the air compressor. You can use a pulley arrangement instead of my "coupler" idea. I never left them coupled because neither was bolted down in any way. I had a 2x4 under the single phas e motor to get the heights close.
Even if you plan to run both machines at the same time, you shouldn't have any trouble. When you turn on the second machine, the first machine will sort of act as a second rotary and add to your first rotary.
