With clipless pedals, there are quite a few different manufacturers / makes, none of which are compatible with the others. They all work in essentially the same way - you have a piece of metal or plastic, called a "cleat", attached to the bottom of your shoes. These click into the pedal, sort of similar to the way a skiboot attached to a ski.
Each different type of pedal has different cleats, and they attach to your shoes in different ways (as far as I know they're all screwed onto the sole of the shoe, but the number and position of the screws differs from make to make). So if you have, say, Look pedals, you need Look cleats too; and with your Look cleats, you can only clip into Look pedals.
Most shoes can accomodate most types of cleats, so if you buy some shoes then further down the line you decide to change pedals, you shouldn't have to buy new shoes, you just swap the cleats.
You generally get a pair of cleats with your pedals when you buy them, and you can buy spare cleats if they get worn out, you buy a new pair of shoes or whatever.
The most common types of clipless pedal are:
Look
Time
Shimano SPD (designed for mountain bikes, though they can be used on road bikes too)
Shimano SPD-SL (Shimano's road type of pedal)
Speedplay
Egg-beaters (more common on mountian bikes, but again can be used on road bikes if you like)
Some people will bang on about one type being better than another, but I honestly don't think there's much difference between them so I'd say just pick some you like. For triathlon I'd suggest choosing between Look, Time, Speedplay and Shimano SPD-SL just because they're designed for road bikes. You should be able to get some decent pedals for under 50 quid.
Changing pedals is simple. If you look at your bike, where the pedal meets the crank arm, there are a couple of flat areas; these are for a pedal spanner (basically just a normal spanner, but very thin so it's easy to get into that bit of the bike). You can buy a pedal spanner for a couple of quid. You simple unscrew the pedals and screw your new ones on, making sure they're nice and tight; and making sure you get the right pedal on the right crank arm! It's a very simple job, all pedals have the same size screw so there's no worries about compatibility etc.
Finally, for shoes I'd say look for something that's comfortable. You want them to be reasonably tight (far tighter than running shoes), but obviously not uncomfortably so.
You'll want either road or triathlon shoes; these have smooth soles (as opposed to mountain bike shoes which have a tread on them). Triathlon shoes generally have one large velcro strap, to make them easier to put on in transition; I don't know if this makes much difference to the non-elites (I'm a triathlon newbie so no personal experience). Most road shoes have two or three velcro straps, or bizarre ratchet things, but I don't think it really makes a great deal of difference. Check that the shoes will let you attach the type of cleat you want - most will, but it's worth just double-checking (the bike shop staff should know).
Sorry for the overly-long post, hope it helps.