What's the STARTING torque ? And as a secondary question, what's the total power ?
If you don't have to start against a load, then you can use most sorts of motor. If it must start "in gear", then you probably need a "universal" motor, i.e. with brushes, rather than an induction motor. These are easiest to find anyway.
I don't think an electric drill or saw is a good idea for starters, but a cheap router will do 4,000 rpm easily and comes with built-in speed control. Some saws will get you to almost 4,000 and you can add the speed control.
And forget using a variac for speed control - save it for the "electric gherkin" demonstration (Google for "electric pickle"). The way to do it is by phase control (light dimmer, with a few extra bells and whistles on). Light dimmers are prety rubbish (400W max, most are only
250W and they don't take kindly to motor loads either). However someone like RS sell a wide range of ready-made phase control modules (just add a variable resistor) and some of them are cheap (even from RS). If you have a big induction motor you can't do this, but if you need something that big then find a cheap 3 S/H phase motor and buy a cheap(ish) VFD (variable frequency drive) from eBay.