It is possible to get a basic, yet decent, stereo system in the roughly £300 to £400 range. Though, of course, the more you spend the more you get.
In general I would recommend amp of 40 watts or more. I had a 40w/ch into 8 ohms Pioneer amp for years, and it served me very well with a wider range of speakers. But, 50 watt or better is...well...better. However, the closer you get to 100watts, the more rapidly the price rises. A decent 100watt amp is going to be £500 or more. But there are very reasonable amps in the 40w to 80w range.
Amp power ratings -
First, you want power rated to 8 ohms to be able to fairly compare amps. Next you want fractional percents of distortion, usually rated as THD (total harmonic distortion) . SO, 10% THD = Bad, 1% THD = not so good, 0.1% THD = acceptable, 0.01% THD = excellent.
Now you will see other power ratings such as DIN, EIA, Dymanic, Peak, Music, all of which are valuable, but only when given along side a basic continuous (RMS/FTC) 8 ohm power rating. The RMS/FTC power rating is very demanding and while it is a sure test of an amp, it doesn't reflect real music conditions as accurately as DIN or EIA. But both together can give you a fair impression of an amp.
Next, is the Ohm rating of the power. Lower ohms automatically mean higher power, so many manufacturers will use 4 ohm or 6 ohm rating to inflate their power ratings. You need 8 ohm rating for a fair comparison between brands.
However, when given with 8 ohm ratings, the 4 ohm rating can tell you a lot about an amp. Theoretically, mathematically, 4 ohm should be twice the 8 ohm power, though in reality that is rarely true. This can be due to a variety of reason. One might be that the power supply is weak. It does fine at 8 ohms but runs out of current at 4 ohms. However, with may modern amps, there is additional protection at 4 ohms, and that might limit the apparent power rating. Still, the 4 ohm power should be noticeably higher than the 8 ohm power.
Personally, I rely mostly on the RMS/FTC/continuous power rating at 8 ohms to tell me whether an amp is going to perform the way I want it to. Other are more inclined to look at the DIN/EIA power. Though realistically, we should all look at both.
Amp are not 8 ohms amps. That is, when you see 50w to 8 ohms, that doesn't imply that the amp will only work with 8 ohm speakers. The 8 ohms aspect is merely a reference point for the rated power. As I've said, based on pure math, low impedance results in higher power consumption. But, high power consumption does not mean a better amp or better sound. It is really all about voltage and current, not power.
Typically, any amp worth having, which includes nearly every amp made, will handle any combined per channel load in the range of 4 ohms to 16 ohms. If you go below 4 ohms, the current demands get to high and the amp over heats and shuts down. If the load impedance get to high, above 16 ohms, the amp becomes unstable as starts to self-oscillate. Self-oscillate is just a fancy way of saying the amp will sound like 'feedback', a high pitched squealing sound.
The amp will 'clip' or reach its limits or ceiling based on available voltage, and the ability of the amp to deliver current at that voltage. If the current capacity fails, then the voltage will fall resulting in less power consumed. So, a given amp driving 8 ohm load, and the same amp driving 4 ohm loads, still have the same voltage and current limits. To get more voltage and hopefully more current, you need a higher powered amp. My point here is that while the power consumption seems higher if you have 4 ohms speakers, the real gain is very slight, and since the voltage limit is equal or less, you really don't gain anything.
To illustrate my point here are several power rating with the corresponding voltage limit to an 8 ohm load - V = SqRt(P x R)
50w = 20 volts
100w = 28.3v
200w = 40v
Notice a little bit of voltage increase gives you a lot of power increase. Double the voltage (20v vs 40v) give you FOUR TIMES the power increase.
Speaker power and impedance -
Speaker power is, more or less, the limit for that speaker. It is the most power you can use, not the ideal power. Likely you can run a 100 watt speaker just fine on a 40 watt amp.
Now some speakers give a range of power as in 25w to 100w. That means the manufacturer is recommending that you do not use these speakers on amps of less than 25watts, and that you don't use them on amps of more than 100w.
In reality neither of these is an absolute limit. If you needs are modest, you can probably get by just fine with a 15 watt amp. Further many people put 100w speakers on 150w amps on the assumption that you are never going to run your amp at full power. This usually works out fine AS LONG AS you understand and respect the limits of your equipment.
A speakers rated impedance is the sort of impedance of that speaker. Typically the impedance will drop to about 0.75 of the rated impedance and can go as high as 10 time or more of the rated impedance. But overall, you can consider the rated impedance to be a fair representation.
The impedance matters because it reflect how heavily it is going to load your amp. This is especially critical if you are going to put more than one speaker on each amp channel.
Most speaker can be taken at their rated impedance, but there are a few, though thankfully somewhat rare, speakers that can have extreme impedance swings. I recall seeing one speaker, a very large floorstander, that had a rated impedance of 8 ohms, but had a side note that the impedance could drop as low as 3.2 ohms. To run that speaker, you need a substantial quality amp, and you can only run one speaker per channel, even though the overall or nominal rating is 8 ohms.
So, with a few rare exception, any speaker will match any amp. When using multiple speaker per channel, we must make sure that the nominal total rated impedance doesn't drop below 4 ohms.
Now there are a few rare amp that can tolerate lower load. I think maybe NAD is rated a 2 ohms, though I wouldn't recommend running it at that load. But you could probably safely use two 6 ohms speaker per channel or a 8 ohm and a 6 ohms together.
There are high powered professional expensive amps that will easily handle 2 ohm load though. But few consumers ever encounter them.
In short, look for an amp that is 40 watts or more to 8 ohms. That amp will handle virtually any speaker that you are likely to buy.
Steve/bluewizard