pre-amp - whatever you need to shape your tone, plus maybe some basic functionality for ringing out whatever room you are playing in.
to my ears, tubes overdrive into a nice fuzzy saturation. silicone tends to be a bit more metallic and edgy sounding.
power-amp/speaker area - balance of wattage and speaker area to achieve your volume requirement, plus a little headroom.
tubes require a bit more TLC, but can add a natural compression. solid-state has a few different types, some are beefy and powerful, some are super light. i've heard people complain that the digital amps sound sterile, while others bless them for instant power.
speaker-type - again whatever you need to shape your tone. bigger cones aren't as articulate in the high-end response, and they may also be slower to respond. smaller cones are faster and can articulate better. depending on cabinet, any driver, even the best, can have a boomy or nasal character to it. look for a cabinet with thick sidewalls, strong bracing and internal padding. A solid box will not add any overtones of its own. Only the speakers/ports/baffles will be creating the sound.
look for a grille that doesn't vibrate.
neodymium vs ceramic/ferrous - weight is the biggest issue. I cant tell the difference aurally, though some people report huge differences. i'll leave elaboration to them.
Depending on where you practice/play, you might also want to find a set of gear (rig) that is capable of creating the tone you prefer at low and high volumes. e.g. you may achieve a great sound with the gain cranked, but that can be a hindrance when practicing at 2am. in that case you might want to look for something with a master volume as well.
The more components, connections and cables you add, the more you introduce potential sources of noise.
I would suggest if you're starting out, to get a combo. Pre-amp, power amp, speaker all in the same cabinet. If you need some more serious fair, a head (pre-amp/power amp) and a large cabinet arrangement should fit that need. Unless you're going on tour or have a fair amount of disposable income or really like tweaking things, you probably won't need a rack with separate effects, pre-amps, power amps and crossovers. Keep it simple is a decent rule.
Summarily- head to a music shop, play through everything, pick what you like that's also practical (i.e. not the amazing 810 that wont fit in your bedroom).
it's more of an interactive thing than something that you can nail down to each component and rate or order. With a killer pre but no or a crappy power section, well, you're outta luck. With a killer pre and power section but no speakers to send it though, well, again, you're out of luck.
