You don't need to spend bundles of cash on all the latest tri gear. A few of the basics are all you need to get started. It couldn't be simpler:
Swim
Novice events tend to be pool-based, although some may involve open-water swims. The type of event will affect what kit you need. A swimming hat lowers water resistance and saves you vital seconds in the water, so it definitely counts as a triathlon essential. You can pick them up for a couple of pounds in any sports store and they're worth it.
Goggles are a godsend when you're swimming in a pack of enthusiastic triathletes. Being able to see what's going on is the difference between getting stuck in the pack or making a breakaway lead. Cold British open water swims mean you can't overlook wetsuits - they're compulsory with water temperatures below 14 degrees. Summer is officially the triathlon season but a full-length wetsuit is still advisable.
Bike
Nobody is excused from wearing a helmet, so you'll never see a triathlete riding without a lid. Modern helmets are reasonably priced, simple to use and they give the best protection to your most important parts. One nasty tumble is all it takes.
You don't need a purpose-made tri suit to compete in, but something close-fitting and comfortable and, if you are taking part in an open-water swim, that can be worn under a wetsuit is ideal. A singlet and shorts will serve you just as well, but extra padding in the saddle area is desirable.
A bike has to count as an essential piece of triathlon equipment, but until you get to a more advanced level you don't have to worry about the quality of your bike. Drag your old one out of the shed, but be sure to give it a good service - punctures could almost certainly be the end of your race.
Cycling shoes are a luxury if you're just starting out, but you definitely want shoes that are easy to get on and off during transitions. The advantage of cycling shoes is that they attach to the pedals giving you better cycling stability and power.
Run
Again, there is no real need for specialist running gear at first. Swim, run and bike kit can double up; just make sure that the outfit you choose to wear is comfortable, even when you've been cycling in it.
Shoes are the most important part of your running equipment. If your feet are well supported and comfortable, it will make your run seem much easier. Check it out with a running shoe expert before you buy, as individual running styles dictate your trainer requirements.