What kind of amplification do I need for gigs?

Hag01 you probably haven't had an answer because this is primarily a pianoteq forum concerned about it not about 'other musical issues' so much. I'd also add you haven't specified where you are (ie what good is recommendation for something good in New Zealand if you are in Finland?) or what your budget is (I understand Bose make a good but very expensive kit that does what you want but if the budget will only go so far as a Roland cube there is no point recommending it).
People here may weigh in on these things but unless it's a pianoteq issue your probably better off raising it in another forum - I would suggest having done some reading of the old post and threads there you try with a more detailed question eg the budget issue and whether you will be playing post punk thrash or Neo classical semi acoustic music Sounds on Sounds forum which will likely get you a better response to your question than here.

But what I most need to know is: Would a keyboard amplifier(connected to the computer) do the job?

I can only give a subjective opinion, but I've tried various "keyboard" amps, including most recently a Roland KC 550 and none seem to be in the same league as my QSC K8 single PA speaker. I'd go with a PA, and I'd get an external sound card between the computer and the PA, myself I use a Presonus AudioBox iTwo.

The ElectroVoice ZXA1 (which I own) is ideal for this purpose.  It's sold as a "stage monitor", but works well as a small PA system.  There are independent "Line" and "Mic" inputs; the "Mic" input has a preamp, but no phantom power, so you can use any dynamic mic.

It weighs about 20 lbs (9 Kg), has a horn-loaded tweeter and 8" woofer.   The amp is rated at 800 watts, but I don't think it can put out that much power continuously.  Frequency response is quite flat, down to its low-frequency limit of 60 Hz (-3 dB) / 48 Hz (-10 dB). 

For an audience of 100 people or less, it's loud enough, IMHO.   

My preference is to put it on a lightweight speaker stand, about 6' high -- e.g. "On-Stage Stands SS7761B".  You can rotate the tweeter to get 90 degree (horizontal) by 50 degree (vertical) coverage.   

There are similar PA/monitor speakers from other makers.   People who have used guitar amps and "keyboard amps" often complain about "coloration".  The PA/monitor speakers seem to be flatter in their frequency response.

.     Charles

PS -- Public transit?  You may have to _really_ compromise on woofer size, power, and total weight.

I use a SpaceStation v3 amp for gigs also, and love it.  However, it is 40 lb (18kg). The original poster seems to have moved on, or perhaps reconsidered his needs, but his request was for advice on amplification he could take to gigs on public transportation. Most powered monitor speakers are also going to be too heavy for this application. This is why I suggested one of the small and relatively neutral amps designed for acoustic guitar and other acoustic instruments.