AC power supply for Arduino and relay

I would like to design a power supply to power an Arduino MCU from 120V AC power. The MCU will control a relay which will also be hooked up to the mains power, so that the MCU can activate the relay and turn a pump on. The Arduino (specs: http://arduino.cc/en/Main/ArduinoBoardDuemilanove )
operates at 5V DC and recommends an input of 7-12V. Given this range, how do I choose what transformer to use? Do I want 7,9, 12? My goals are to keep cost down, but more importantly keep heat to a minimum. Am I basically going to be implementing this: http://www.sparkfun.com/tutorial/Power%20Supply/linear_powersupply.jpg
or are there advances in power supply design that I should take advantage of? I have seen some power management ICs from Maxim, Power Integrations, etc, but they still seem to need a transformer, so I am not sure of the benefit. How do I go about choosing the correct thermal cutoff/fuse and correct diode and filter cap values? Thanks.

Any thoughts or advice?

Skip the transformer and find a 7 to 12 dc wall wart with enough current for you uc and relay. 100 ma should do it for the uc. Relay should have the data on it.

If I use a wall wart, I won't have 120VAC for the pump being controlled by the relay. My thinking was that I would be able to use one wall socket for everything. Is this atypical?

Well, we like for our "n00bs" to stick with low-voltage (<50v) until they get some experience under their belts. If you're working with mains power, things can go bad very quickly, up to and including getting yourself killed.

There is little risk when working with low voltages; at worst you might burn a finger from overheating a component and grabbing it. The quality of workmanship and components are not nearly as important with the low-voltage low-power stuff as when working with mains power. With the latter, everything becomes critical; you must ensure that everything is UL approved and meets NEMA specifications for the enviornment where it will be used, and the power and voltage ratings meet or exceed the limits of the breaker that protects the circuit. The enclosure must be properly designed/selected and grounded if metallic.

If you are a novice to electrical projects, you really shouldn't attempt such a project without direct supervision by someone with a good deal of experience.

I appreciate the concern. However, I am not a 100% newb. I have education and experience in the area, however I am a few years rusty on component selection. I have taken proper precaution, with my relay and outlets more than capable to handle the amperage of the load. I am using a plastic project enclosure, and I have used the same type for past projects. I understand the risks and would appreciate and advice you could offer.