There are no 3.5Hp VFDs, typical sizes would be 1, 2, 3, 5, 7.5, 10, 15 and 20Hp in the range that most people use them. Typically those up to and including 3 Hp are available in single phase models, very few are single phase input in the 5-10Hp range (up to 5 Hp Yaskawa and up to 10 Hp Invertek). Most 3 phase VFD's can be run on single phase but need to be derated on their output current rating, these days the usual factor is to divide the output current by 2, but it varies by VFD model so you always need to refer back to the manufactures derating. There are some cases where you might want to oversize a VFD, but in general as long as the VFD's rated output current is higher than the motor full load amperage and factoring in any derating and the type of load (ND, HD) you do not need to oversize it. If you have a 3 Hp motor on the P&W lathe then I would recommend one of the following VFD's:
Hitachi WJ200-022SF rated output in HD mode is 11A
Teco E510-203-H-U rated output in HD mode is 10.5A
Invertek ODE-3-220105-1F42 rated output in HD mode is 10.5A
Yaskawa GA50UB012ABA rated output in HD mode is 11A
Wolf Automation often recommends Fuji Drives, I have not used them but find they are a bit quirky on some of their programming functions. They are reasonably priced and a good option for larger or difficult loads where one needs to oversize the VFD. Many people use the Hitachi drives, they are robust and reliable. The biggest single phase rated model is the WJ200-022SF, if you wanted to run say a difficult start 3 Hp load motor then one would use the the wj200-055LF which is a 7.5 Hp 3 phase input VFD so in single phase input derated mode would equate to ~3.5 Hp. Also if you look at the output amps/duty
As far as electronic braking, it depends on how the lathe is used and whether you are using the clutch/and or electro-mechanical braking system. The other thing to think about is if the machine is running and you press the E-Stop how fast will the lathe stop. SInce a braking resistor only costs around $60, I would install one as an added safety feature.