I assume you're the singer then? When you say you need an amp do you mean you already have speakers (In which case what are they?) or are you assuming they come with the amp?
Tube amp: Amp with valves in it.
Solid-state amp: Amp with transisors in it.
They both need speakers and you can buy both of them with or without speakers.
For a PA (Vocal amplification) you need a separate amp and speakers because they sound best if you have a speaker on either side of the stage. Solid-state amps are best for vocals because tubes/valves colour the sound unless you buy a very expensive tube amp, which are absolutely the best.
If you're just starting out and only need an amp so you can be heard in rehearsals then buy a cheap solid state amp with built in speakers designed for keyboards or acoustic guitar. Bass amps are OK too as long as they're designed for 'Slap & pop' style players (They usually have little speakers in the corners as well as the big one in the middle). Just remember that before you start doing big gigs you're going to have to buy an amp + speakers set up.
There are a lot of good cheap mikes about, take a look on eBay, but once you start performing you may need to go to a music shop for a better one. For some reason all the best mikes seem to have started life in Germany, so look out for names like Beyer, Shure, Sennheiser and so on...
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When you say you need an amp do you mean you already have speakers (In which case what are they?) or are you assuming they come with the amp?