I haven't built one myself but it's on my to do list but having built my own CNC I feel a bit more at ease with engineering and electronics than I did. Firstly, I think you are talking about a motor and not a power supply - you really would only need a power supply to run a DC motor, an ac motor will run off the mains. You need a low speed motor - the average standard equip ac motor will be too fast - you can of course gear it down with pulleys but generally its better to get a motor at the correct speed - 1300 to 1700 rpm range. Also you will need to take into account what kind of mount you will require to fix your motor to your machine frame - this will depend on your design and it will bear a lot of sheer force so needs to be solid, a foot mount or a flange mount is common - you can get some that do both. Expect to pay over £100 for a new 1/2hp to 1hp motor. I think 1/2hp (320w) is underpowered personally - chances are your motor will outlive your machine and can be repurposed later for other machines or a rebuild so get a good one. BTW, there is really no such thing as a variable speed AC motor (not by varying voltage anyway). Of course you CAN vary the speed of a AC motor using a variable frequency drive (no that's not the same as a flux capacitor
) but thats getting expensive and they are complex to configure to the motor or they will trash your motor instantly - trust me I learnt this the hard way.
The simple and tried and tested solution is to use the motor and speed control from an home fitness treadmill. 99% of people who spend £400 to a grand on one only use it for a week and then hang their clothes on it for 2 years so they come onto ebay all the time for £50 and you will find one locally I bet. From this, you can glean a perfectly suited, well powered motor, with speed control, pulleys, steel rollers, quality bearings and even a perfect flatbed - google for treadmill flatbed sander, its been done many times. Otherwise, you should consider using a DC motor which can be variable speed simply by changing its voltage - something like this will control it very well - it also acts as a rectifier
https://www.amazon.co.uk/gp/product/B00 ... UTF8&psc=1
Be sure to match the speed controller voltage to the DC motor voltage if you follow this route. The downside of this approach is that DC motor in the 1hp range are expensive and finding one to match the voltage of the speed controller might be tricky.
I'd go with the AC motor - buy an old treadmill and knick its innards and gubbins and I'd also utilise the digital control panel. Hope that has helped and not confused you - I'd like to see what you have done and do as I plan on doing the same when I get the time.