Thanks for the replies guys.
This is by no means a comprehensive reply, but it's just what I'm up to and found out so far. I hope it's reasonably correct and helpful...
I have decided to mine using my ATI graphics cards, while I'm using the machines during the day.
I'm currently running GUIMiner on Slush's Pool (with Stratum proxy enabled) and BTCOxygen (yes, really), while I get some better systems set up.
Since signing up here, I have made nearly a whole Bitcoin. I know, wow!
I'm never going to become a Bitcoin Millionaire, but I might make a few dollars here and there. It's winter in the UK atm, and while the main system is mining it produces just enough warmth to take the chill off the office.
I'm currently doing about 500Mhash/s spread across two pools.
It's a good idea to have two or more pools in case there is a problem with a particular pool being offline - that way the other pool is used as a fallback to allow mining to continue and not waste cycles.
You will need to get a wallet, either online or offline, in order to store your Bitcoins. You will also need to generate an "address" for that wallet and register it in order to be paid your mining rewards.
To any other newbies out there, be prepared to spend lots of time getting nothing much in return. There are many other miners out there who are grinding through awesome amounts of data (thousands of Ghash/s) that the chance of you finding a valid block (25 Bitcoins) by solo-mining is pretty much non-existant. Think of how likely you are to win a national lottery and you start to get a feel of what your chances of success are.
Pool-mining is a way to get some pay out for shares processed. You get a share of blocks found in the pool that you are mining in. The larger the pool, the better chance of a payout, but the smaller the payout as it has to be shared amongst more miners on a shares-processed basis. There are quite a few schemas used in different pools. It's up to you to research what scheme you want to take a risk with. Stratum support in the miner that you use is handy to have. Not going into Stratum here. Search the forum, etc.
There are also Proxy Pools such as BTCOxygen. These are a way of getting a fixed output per share processed. The jury seems to be out as to whether this is a good thing or not as far as I can tell. Some people are not happy with this particular pool, or the person running it. I'm taking a gamble and see what happens.
Oh, be aware, that most (all?) pools charge a percentage "tax" on your mining payout to cover their costs and make a bit of cash for themselves.
Hope I have got things right. Please be kind in your comments if I have said anything daft, and I will edit accordingly.
Whatever you decide to do, I wish you well.