Just the sheer amount of brand names alone can make someone's head spin, much less the amount of models in one single brand. To cut through all those choices, one needs to first ask themselves a few questions to narrow down the playing field. With this kind of ammunition in hand, you'll be better prepared to face the shelves of guitar amps and find the one that makes your guitar sing the way you want it to.
1. Ask yourself and make a note of what types of music you like to, or would like to play. Do you want to play country? Do you prefer heavy metal? Do you have a wide range of music genres that you'd like to be able to play? Some amps sound better for one particular music genre than they do another. If you you have a wide range of musical taste, than you'll want to look at an amp that itself can do a broad range. For example, with jazz, many players desire a clear, clean tone, which can be achieved with a Roland JC120 amp. Heavy metal players like to use amps which can give out a heavy, distorted tone like the one possible with a Mesa Boogie Triple Rectifier. Some amps, such as the Roland Cube Series or the Peavey Vypyr Series, can "model" many different types of amps, making these amps extremely versatile and able to play many different types of music.
2. Decide if you plan on playing gigs or shows with this amp, or if this is something that you'll only use for practice in your bedroom. Maybe it's something that you'd like to be able to move from the bedroom to the stage. If you're going to be playing with a band, you'll want an amp that will be able to produce the volume to help you "cut" through the rest of the instruments and be heard. This becomes slightly less important if the place you gig or plan to gig at has a PA system which a sound engineer can "mic" your amp to. With an available, in-house PA system, it's possible to even play with a band with small amps. If one's not available though, then you'll need something with a good amount of wattage to it. Depending on the type of music, size of the venue, and loudness of the other people in the band, this can be anywhere from a 30watt to a 100watt amp (in very simplistic terms, the higher the wattage, the louder the amp.)
3. Calculate how much you would be willing to spend on an amp. Also, do you have anything that you might be able to possibly trade in or sell to add to your amp fund? Are you willing to look at and possibly purchase used (and thus possibly save some money) as opposed to new? Higher wattage amps will tend to be more expensive than lower wattage amps. Name brands also come into play, with hand-made amps generally fetching a premium. After calculating how much you have to spend, see what brands and models fit within your budget, then start narrowing down from there.
4. Gather all the information that you've collected from the first three steps and do some research online. Ultimate-Guitar.com contains product reviews and forums from which you can get plenty of information and opinions on amp possibilities. Although many of the reviews and opinions may vary from person to person, they can still provide a nice base for you to begin your search, both for types and brands of amps. You'll be better informed and able to arm yourself with a list of possible models to try when you get to the store to take your final step, and begin trying some amps out in person.
5. Bring your guitar with you to test out amps at the store. Most places are more than willing to let customers test out amps using their own equipment. If not, move on to a different store. The reason why you want to bring your own guitar with you (or if they have the exact same model guitar, use that) is so that you'll have a good idea of what it will sound like when you take the amp home. Different guitars will each have a different tone from one another, which can be blaringly obvious depending on the amp. A Gibson Les Paul will sound much different from a Fender Stratocaster when played through the same amp. Even two Fenders can sound different due to different pickups, woods, etc.
6. Check the store's return policy. Even after testing an amp at the store, you might find it sounds different when you take it home. That's because the acoustics of your home (or playing area) can be vastly different from the store's.
It may seem like a lot to keep in mind, but when you consider the importance of getting the right amp that fits your style, it can save a lot of headaches and money in the long run.