The amplifier you use will depend, again, on the style of music you want to play and you budget.  It will also depend on the size of the proposed venue.  The are some things to consider when purchasing an amp: the power, whether to buy valve or solid state and the brand or style.

Power
Traditionally, amplifiers were made with valves (tubes in the US), which was the technology available at the time.  The downside (at the time) was that when you turned them up loudly, the sound broke up (distorted).  We now see this as a good thing and most popular music guitarists use this breaking up as part of their sound, whether this is mild overdrive (crunch), such as found in blues and country, or distortion/extreme distortion as found in rock or heavy metal.  If the amp distorts easily as you turn it up, it doesn’t have much ‘headroom’.  If you turn it up to half-way and it still sounds clean, it has plenty of headroom.  If you play jazz, you want a clean sound, so plenty of headroom.   I have a 10 watt Cornell amp which I use for small gigs.  It goes from 10 watts down to one quarter of a watt, which is still too loud for courteous home practice. 

My main gigging amp is 20 watts.  I usually mic it through the PA, so it is suitable for most venues.  I had a 50 watt Marshall Bluesbreaker, but it was so loud, I only ever used it at one outdoor gig.  When I first started going to gigs in the 1970s, guitarists seemed to favour 100 watt Marsahall stacks (separate heads and cabinets).  Even in small pubs.  No wonder I'm deaf!

The biggest mistake made is buying an amplifier which is too big (powerful).  When you’re at home, practising, you won’t be able to turn it up without being very unpopular with neighbours or family, and if you don’t turn up a valve amp at least to half-way, you won’t get a good sound.

Valve or Solid State
So, valve amps give a great sound if you play popular music.  If you want a clean sound, or an amp which is lighter and more affordable, then go for solid state.  These use transistors rather than valves.  Some of them have ‘modelling’ so you can make them sound similar to well-known valve amps or add effects.  When I practise at home I use a tiny Roland Micro-cube.  It wasn’t much money, the sound is fine, it is low volume and has effects built in.  It also can run from batteries, if I want to go outdoors.  You will have to read the amp specs to know whether they are valve or solid state.  Or look in the back of the cabinet!

Brands
There are a huge number of manufacturers of amplifiers, but they tend to have the sound categories of Fender and Marshall, with Mesa Boogie somewhere in the middle.  Other brands tend to have sound characteristics of one of these three.  Fenders have a tone which is somewhat more high-end, whereas Marshalls have more mids and low end.  A  Country or 50s rock n roll player might have a Fender type and a heavy rock player, a Marshall.  These are typical and could just as easily be the other way round.  Use your own ears when you decide.

Other Considerations
As with all equipment, you really need to try it out to know whether you like the sound.  As I said, when you try it out you’re also going to need to be able to turn it up to get a good sound, if it’s a valve amp.  Valve amps are more expensive and less robust.  Drop one down the stairs and it might not forgive you.  Turning the power off suddenly (see sound limiters in Tips n Tricks) can cause valves to blow.  Once again it’s a personal thing, but I don’t think you can compare the tone.  See what you think.

I'm going to be contentious, but in my opinion, if you play metal, you can use the cheapest equipment, because the sound is so heavily distorted.  In fact, the first song I can think of which used heavy distortion was 'You Really Got Me', by the Kinks.  The distortion sound of the guitar track was created after guitarist Dave Davies sliced the speaker cone of his guitar amplifier with a razor blade and poked it with a pin.