I agree with what the others have said, particularly with the idea of getting a second-hand sub (there are plenty around) because it's a shame to spend a lot of money on something that you may not actually even like that much - more than other speakers, different subs produce different results!
Can I just say that the size of the subwoofer is important, and bigger is not necessarily better...! It depends on what you are after. I've had 12", 15", another 12", and have finally settled on a 10" as being most suitable for my tastes (possibly even an 8"!). The main thing is that I don't like R&B, rap, or hip-hop music. Instead I have Fur Patrol (rock), Daft Punk, Coldplay, Live, err, Roxette (!), Dire Straits, Prodigy, umm... and others. It helps if you can narrow this down before you choose the speakers! I want the music to have a 'punch' but it needs to have smooth midrange (vocals) without too much treble (dome tweeters essential). I want to avoid the 'boom' at all costs (I turn my sub level and frequency down so that you can tell it's there but no more, not drowning out the instrumental parts). If you want the boom, that's great - go for a 12 or a 15 - but if you want something that gives a subtle boost, smaller is better. (Also it takes up less space in the boot and you can get away with a cheaper amplifier - see below)
I reckon the first thing to think about is the front speakers. If I had only 50-100 pounds to spend (no pound symbol on my keyboard!) then I would upgrade the front speakers before anything else. Ah that's right, that's what I've just done - I bought some Infinity Kappa component speakers for the front of my Mk2 Punto, because the standard speakers are... well, let's just say they sound better than they have a right to.
My speakers cost under 100 pounds - I haven't got around to installing them yet - and I intend to run them off the original head unit because it has the 10-disc CD changer under the seat and the original 100W (tiny!) 4" subwoofer in the boot. If I change the headunit, I have to throw these out (and I can't be bothered to do that - also, the original curved headunit looks better than aftermarket surrounds/faceplates.) I know that changing the front speakers will give me a much more 'full' sound, and it will be loud enough especially once I've installed some sound deadening to box-in the doors and increase the efficiency of the speakers.
I presume you're starting with something less than this (maybe cassette-only) - in which case, replace the headunit. I liked the Blaupunkt units from about five years ago, but they've gone a bit cheap and nasty now to compete with entry-level offerings from Sony etc. More expensive Sony headunits have Bluetooth, 'stealth' faceplates, and so on. JVC make one that has a 4" colour screen for playing DVDs - but do you need it?
So I can't tell you which headunit to pick - but try to choose something with nice buttons
I've installed perhaps 20+ headunits over the years and I don't feel that the choice of headunit makes much difference to sound quality compared with the speakers and installation. It's more about looks, usability, and whether it does what you need (most have an auxiliary input these days, but maybe pick one that comes with a proper iPod connector cable and controls the iPod playlist, as the iPod is difficult/dangerous to use while driving).
Installation is very important. Speakers mounted properly in a closed area (such as the door when fitted with soundproofing) sound much better than speakers in open-air. I would say it's worth budgeting another 50 pounds per door for sound-deadening, especially in a car like the Punto that is not built as a luxury car.
After speakers and installation, amplifiers are the next item. Bear in mind that the head unit will claim "52W x 4" or some such... this translates to about 18W per channel 'real' power (RMS). Power is not a linear requirement. To get a slight increase in apparent volume (+3dB), you need twice the power, so it is diminishing-returns. A 100W-per-channel amp does not sound twice as loud as a 50W/channel amp. Even 50W/channel is substantially more than the 18W that you started with. Therefore I would suggest to get a 4-channel amp (or six channel as Tris said, but bear in mind that the back speakers are tiny 4" types and I wouldn't bother to amplify them - I'd prefer to have most of the sound at the front). Anyway, with your 4-channel amp, you'd use two channels for the front speakers, and then bridge (connect together) the other two channels to drive the subwoofer. With a 4x50W amp, that's 100W (or a little more as bridged outputs are usually higher than individually) for the subwoofer.
If you have a 12" or 15" sub, you should get a 4x100W amp. That's because you need at least 200W for the larger subs - though your front component speakers may not handle 100W each, that is OK because you can always adjust the levels on the amp. What happens if you don't have enough power to drive the sub, you ask? The amp starts to 'clip' (reach a maximum voltage and stay there momentarily) and this damages the speaker.
More power than this and you need serious cables - starts to add significantly to the cost - very important to have a big earth cable as well as a big power cable. 1000W RMS is readily available but costs five times as much as 200W RMS (appropriately), several times as much for installation, and of course will not be five times as loud.
In my Uno Turbo, I have a $200 (80 pounds) Sony headunit that plays MP3 discs. Virtually all CD players do this now. This is worth considering as you don't want to leave your iPod in the car. It becomes a hassle to take it out every time you park, then plug back in when you return, and as I said before, unless the headunit controls the iPod, it's fiddly to select songs on the iPod as you drive.
My Uno Turbo also has 6.5" Kevlar component speakers of no particular brand, the 10" carbon-fibre sub in a custom spare-wheel-housing boot install, and a small 4x 50W amp driving it all, with modest cabling and cost. The whole thing came in under $800 (280 pounds).
My Alfa 164 has a Chinese-made headunit with a 4" LCD touchscreen that plays DVDs and has a reversing camera. It's also a TV and a Bluetooth phone kit. The controls are awful - TINY parts of the screen to press with a fingernail and Chinese characters appear here and there. It cost under 100 pounds. I haven't fitted an amplifier. The rear speakers are Kicker 6x9s (not my choice; that's the factory fit!) and the fronts are MB Quart components. Again, speakers and installation is everything, in my opinion.
Let us know what you decide on
Cheers,
-Alex
PS. to anyone else who's bothered reading this far. Just a quick note on RCA outputs. That cheap Sony headunit of mine has just the one pre-out pair (left and right), intended for running either rear speakers or a subwoofer (the headunit lets you select one or the other). I thought about it for a little while, and chose 'Rear speaker output' (full range). My amp has a pass-through (two channels have in and out), so the signal comes from the headunit, into the two speaker channels, then out to the (bridged) sub channels. The amp provides the level and crossover controls for the sub. The trick is that the two amplified speakers are at the FRONT, so I have the two rear speakers hooked up to the front headunit outputs. The upshot of all this is that I get by with only the one set of pre-outs and the only 'problem' is that the fader control is back to front - but does that really matter, I ask you... I reckon the extra preouts are a bit of a gimmick
The main benefit is that you gain headunit control over your sub crossover and level, but this isn't really essential as it shouldn't need adjusting often.