The Arduino is really popular, and it is open-source hardware, so there are variations, including the third-party Freeduinos called Bare Bones Board, the Really Bare Bones Board, and the Boarduino, which are very nice for using with breadboards. The standard Arduino is adapted using things called Shields. You can make your own breadboard shield or buy something like this ProtoShield Kit.
The Arduino uses an FTDI USB-RS232 chip or cable. [The standard Arduino has it build in, while the most of the bread board ones use a special cable that has the chip inside, and saves you some money.] There is a built-in driver for Linux, and Mac OS X and Windows users can download a driver. Effectively, this means that the Arduino acts as a device communicating on a serial port, and so it is very easy to communicate with.
To use it, you also download software. It comes with an IDE, an AVR-GCC toolchain, a really nice library, and software to upload your program on to the chip. It hides most of the details from you, and has a great community. It is programmed in a language called "Wiring", but it is really C++.
Lastly, being open-source hardware, there are schematics out there. Indeed, I seem to recall reading that it was fairly easy to build an earlier model. Searching for "Arduino schematics" in your favourite search engine will give you good results.
As for kits, the Maker Shed offers a lot of Arduino-related items in stock. They appear to ship around the world. Some ones of interest include:
The Shoppe at Wulfden (USA) has a nice experimenters kits, and appears to ship internationally.
Solarbotics (Canada) has a ARDX Arduino Experimenter's Kit, a Freeduino Starter Bundle - Ultimate and an Arduino Starter Bundle - Basic (and Ultimate), and appears to ship internationally.
The main Arduino's "buy" page lists Arduino vendors in all areas of the globe.
Other places I would check include Adafruit Industries and Sparkfun Electronics (both in the US).
I spent 13 years designing electronics of this exact nature: three phase induction motor reduced voltage soft starters and variable frequency AC drives. I spent the last few of those years as a VFD applications engineer helping customers select and configure this equipment for various loads and industries around the country as well.
You will not be able to build something that is cheap and safe. The voltages and currents involved are well beyond the safety margin of a hobbyiest, especially someone who is openly avoiding buying commercial units in order to save money. Don't do it!
While the theory behind AC motor control is very straightforward, the detail level work (heat sink sizing, snubbering, gate drive requirements, de-sat protection, motor overload calculations, bus capacitor protection, etc.) can be quite tricky to get down, especially with heavy duty cycling and regenerative power modes which a carnival ride will CERTAINLY be generating. I strongly caution you against trying to build something of this nature unless you have significant experience not only in microcontrollers and embedded systems design but also significant experience in power electronics and three phase circuitry. People get hurt and killed building this stuff.
My first question for you is whether speed control is really required, or if you only require a soft start up and slow down. Do you vary the speed of the motor once it is started? If not, you may be able to get away with a MUCH cheaper reduced voltage soft starter. These units act like three phase light dimmers; they only adjust the applied voltage to the motor. You will not have a lot of torque at low speeds, but with the right design of motor (NEMA class D) you can achieve exactly what you're after with a fraction of the cost and maintenance.
If you really do need to vary the full-load speed of the motor then you are more or less stuck using a variable frequency drive. As you are aware these are expensive and if you buy cheap you are likely to replace them sooner due to your high surge current (they call this "constant torque") application. What I would definitely recommend doing if this is the case would be to contact various manufacturers (Allen-Bradley, Cutler-Hammer, SAF drives, Benshaw, Yaskawa, etc.) and ask for reconditioned units. Ask for a drive capable of delivering 150% rated current for 30s (this is usually known as heavy duty) or size the drive 30-50% larger than your nominal current rating. You will also likely be running off of generator power which is notorious for being undersized and prone to brownouts and surges as the load requirements change with the state of the equipment being run. Drives don't like that (voltage sags cause current spikes as the motor starts slipping and surges can cause you to overvoltage the bus capacitors) and have a tendency to either fault out or blow up.
I am all about the little guy building something and saving a buck, but this is not the type of project to do this on. If you really want to build a three phase AC drive, start with a little 10HP 480V motor with a hand brake on a test bench. You have all the potential for experiencing the pants-filling sensation of an H-bridge failure or a bus capacitor explosion two feet from your head but without the potential lawsuits and loss of life (except perhaps your own).
Best Answer
I've been most impressed with the Pololu range of motors and servos.
Their site has clear specs for each of the parts and other parts to accompany the motor.
Note: Gratuitous plug
Little Bird Electronics is starting to get these in stock if you want cheaper shipping in Australia but it might be a while before the full range is in.