Short answer: There are two types of kegs homebrewers use, your local homebrew shop will probably have just one.
Longer answer:
Assuming your boyfriend is a homebrewer (I assume he is, given the forum you're on) -
The vast majority of brewers use 5 gallon cornelius (corney) kegs. These come in two general styles (pin lock and ball lock). The limiting factor will probably be height - how tall is the inside of your fridge? The shortest homebrew kegs are around 23 inches tall.
If he's not a homebrewer, or he wants to dispense commercial beer, you're probably looking for a sankey keg. See this page for sizes:
http://www.micromatic.com/beer-questions/sizes-keg-draft-beer-available-aid-11.html
If that's the case, ignore the rest of this post.
A kit is a great option for getting started. If you're tight on time, or interested in supporting local businesses, your local homebrew store will almost definitely have some kind of kit to offer. Prices online can be a little lower sometimes, but because of size and weight, shipping prices can often wash out the savings.
Even longer answer:
Historically, these kegs were used for distributing Coke and Pepsi syrups, so most kegs are refurbished/rebuilt, but new units are available too.
To get him set up, you'll need at a minimum:
- a keg
- a gas-in quick connect
- a beer-out quick connect
- gas line
- beer line
- a gas cylinder
- a gas regulator
- a tap of some sort
the keg
Pin lock and ball lock are not interchangeable. The quick connects you purchase will work with one or the other. Right now, pinlocks tend to be cheaper and easier to find than ball locks.
Generally, ball locks are taller and narrower than pin locks, but since the posts can be replaced (at some cost and effort), you may find tall, skinny pin locks or short, stout ball locks
Kegs are often sold as used, refurbished/rebuilt or new.
Used are just that - used, non-refurbished. If you buy used, you or he should clean the keg and replace the gaskets.
Refurbished or rebuilt typically have had their gaskets replaced, their insides thoroughly cleaned and may or may not have been cleaned up on the outside.
New are typically made in the US, Italy or China. Many people will say the Chinese units are lower quality. I haven't used them, so I can't speak to that directly.
prices and availability of used and refurbs vary, but in my area, refurbs cost about 50% of the price of new, and used cost about 10% less than refurbs.
the quick connects
There will probably be one or two options at the homebrew store that fit the keg you've selected. They will have a barbed version, and may have a threaded version. The barbed is probably the easiest for a new setup
the gas cylinder
Most stores will stock a 5 lb tank, some ma offer a 10 lb or 15 lb option. The cost of refilling is low enough that really you should decide what size tank to use based on the space in your fridge. 5 lbs will last quite some time, so this is a good place to save money on your setup.
the gas regulator
you need some way to control the amount of gas coming from the tank. a good regulator will show you the pressure of the gas and include an indicator of how much is left in the tank
the tap
The least expensive option is a picnic tap - this is a plastic tap that is jut attached to the end of the hose - not mounted anywhere. You can also get a metal faucet to be mounted either through the door or on a tower out of the top of the fridge. Towers are a little more expensive and a bit harder to install (or sometimes impossible, depending on the refrigerator), but many people prefer the look.
see this thread and its links for even more info:
https://www.homebrewtalk.com/showthread.php?t=43347