Appreciating that the model numbers we talk about here are relevant to the time this guide was prepared - March 2009 - the principles of the graphics card market nonetheless remain roughly the same, and sub-£50 has always been budget-land. That said, we'll keep mention of individual product names down to a minimum!
You'll find that a budget graphics card does have its merits, though. One generation's budget was a previous generation's cutting edge, and this does prove true to an extent here.

You'll find that a modest graphics card can play old games very easily and generally releases some of the graphical pressure off a computer. They also have low power demands on a computer, and thus - unlike some - a graphics card purchase wouldn't in this case necessitate a good look at your computer's power supply.
And there's one further benefit: graphics cards at this end of the market often have 'passive' cooling, in that they don't rely on a noisy fan to displace the heat they generate.
Furthermore, prices start from as little as £27 for a Club 3D-branded Radeon HD 3450 with 512MB of memory (if you want to take the ATI path), or there's a 9500GT with 512MB of memory for around £40 (if you prefer NVidia products).
Always check, incidentally, particularly at this end of the market, that the memory is legitimately on-board the product itself, rather than relying on 'shared' memory. What the latter would mean is that your graphics card would be helping itself to some of the main system memory to go about its business, and that's going to rob Peter somewhere down the line to pay Paul.
Start spending more and you can start doing more. In fact, a graphics card costing between £50 and £100 could be just the job for a media PC (although perhaps more investment might be an idea should high definition be required). Save for high end games there's not too much a card in this price band will struggle with, even if sometimes settings have to be compromised.

Just squeezing into this price bracket, with a bit (okay, a lot) of savvy shopping, is NVidia's GeForce 9800GT with 512MB of memory, for instance. This was, fairly recently, regarded as a bit of a beast of a card, and it still cuts the mustard where performance is concerned. Again, you may need to tweak some settings down to keep on top of things, but this is a frighteningly capable piece of hardware, and the fact that it can be bought for just under £100 is quite something.
Go a little further down the budget tree, though, and there's still little reason to complain. Take ATI's HD 4650 and 4670 lines. Neither is cutting edge, but both deliver some really good all-round performance, all at around a £60-70 price point. Spend a bit more, and head towards the £90 mark, and you can get the earlier generation HD 3850 Pro card, with 512MB of memory. This was a bargain on release and remains a bargain now, capable of shifting around games that you wouldn't expect it to be capable of handling.
£200 is, for all but the most committed and cutting edge, the most any modern user really needs to spend on a graphics card. Here you should be comfortably able to get a board that can deal with games, high definition playback, graphics and multimedia work, while getting barely a murmur of complaint in return. Obviously the more you spend, the more you get. But this is sweet spot territory, where cash spent and performance garnered meet joyfully in the middle.
Take the HD 4850 and HD 4870 lines from ATI as an example. While the latter is the most powerful, the former has shown itself a very strong performer in both multimedia and gaming (running the majority of top titles). Clearly, if the budget can stretch to the 4870 then there are benefits to be had, but for around £120, the HD 4850 in its own right is a very impressive card (the 4870, meanwhile, sells for around £175, with the price heading northwards depending on which variants you opt for).
If you prefer NVidia, then here's where you'll find the lion's share of strong 9800GT variants, which continue to prove popular. Older 8800s - and there's always joy in going shopping around earlier generations of graphics cards - are also worth snapping up, and can shunt around pixels and polygons with some majesty.

Above £200, there aren't rampant day to day benefits you'll see from spending an enormous amount of money on a graphics card, but if you have to have those settings tweaked to the max, and you need the best, then fair enough. It perhaps goes without saying that a card in this budget should handle everything you can reasonably throw at it, and a few unreasonable things too. But heck, we've gone and said it anyway.
Now read our Graphics Card reviews