Hi Malachi.  Welcome to the Fiddlerman.com forums.

Easy question first.. No it doesn't take a special amp.  Most of the ones that can sound decent with an electric guitar could sound decent with an electric violin.  Most of the same effects pedals work for either, as well. 

You can get distortion the same way that you do with electric guitar.  Either a pedal or overdriving the amp. 

Should you learn on a "pure acoustic" violin first?  In my opinion, only if you want to be able to play one.  Much like with guitars, there are some differences between acoustic and electric in how they are played.  What I would suggest is getting the one that you actually have the most interest in first.  If you want to play electric, go with electric.  If you can't get the sounds that you are after out of the instrument, then you aren't as likely to stick with it and keep your enthusiasm going.  

How to go about learning it?  That's a trickier question.  You can find tons of websites dedicated to teaching folks how to play "classical" music, bluegrass, old-time and etc.. But little or nothing that I've seen so far on playing metal, rock or etc.

Fortunately, notes, scales, beats and etc are the same.  So for learning the bare basics for playing the instrument, you can use basic educational materials for "classical" or bluegrass, etc.

Do you have any background in maybe playing another instrument in metal/rock bands, like guitar or keyboards?

There are so many options on gear.. Much like if you asked the question on a guitar forum, there could be hundreds of answers, at least.

What I'd recommend first is checking out Pierre's review of one of the Cecilio electrics.  More than a review, it explains a bit about electric violins and he demonstrates some effects and etc, which just txt in a reply really can't do so well.

http://www.youtube.com/watch?v.....8CCGI#t=73

In most cases, changing the strings is a good idea.  Even if it was strung with something decent, usually it will have sat in a warehouse and they can already be pretty stiff and dead. 

If you're looking for something tiny to just hear with something like a set of earbuds, Vox also puts out the "amplug" series.  Very small, they'd fit easily into pretty much any violin case or gigbag.  They don't cost a lot, they do a decent enough job, and they hold up well.  Their limitation is that, like that tiny amp you mentioned having bought before, they're a bit limited so far as flexibility.  

I sometimes use the amplug version of a Vox AC30 for guitar.  That particular one probably isn't the sound you're looking for, but their "classic rock", "metal", or "lead" ones would likely have at least some of the sounds you seem to be thinking of.

That'd be towards the small and inexpensive end of the spectrum of options you might consider.  As gws already mentioned, there are also some multi-FX pedals with a headphone out that would cost a bit more, but would do the same basic job and allow you more flexibility to experiment with different effects and tweak the sounds.

Software amp and fx rack emulators, like you already mentioned, can also be a good low-cost platform for experimenting and trying different FX and emulations of amps and speaker cabs.  The problem with them is that they usually have "latency".  That is a tiny delay between when you do something and you hear it.  Depending on your computer's speed and etc, it may be low enough to ignore, or enough to be annoying or unplayable in practical situations for stage, jams or even practice.  Even so, the free ones can be useful at least for getting an idea what fx or etc you might actually want. 

The sky is the limit when you're talking about gear for rock or metal.  You're probably going to want to start kind of small until you learn how to play, at least.  Otherwise, you can sink an awful lot of money into something that ends up just collecting dust if you don't stick with violin more than you did with guitar.

Personally, I am not a big fan of the little "practice" amps with one or two watts and a small speaker.  Most of them don't sound very good, and they are still often too loud to be able to practice late at night and way too small to jam or gig with.  For late night, I use a headphone amp, and the rest of the time I use this:

http://i96.photobucket.com/alb.....4e6235.jpg

That's a vintage (old) 60 watt tube/valve amp with three 12 inch speakers in the cabinet, and sitting on top of it is a compressor and a multi-FX unit.  It can go quiet enough to practice for all but the very late hours of the night, but is enough that I could gig or jam with it and it would be plenty for most situations.  For violin, I'll usually use that and a volume pedal.  For guitar, I'll usually also use an overdrive box and maybe another multi-fx. 

For recording, I can mic that, or I can run the line-out from the head into my mixing board and then into an audio to usb interface box to get it into the computer.

But what I'm saying is it is a matter of trying some things and finding out what you like and what sounds you want and what works for you, and then finding some gear you can afford that can deliver it. 

The suggestion gws made of a multi-fx pedal with a headphone jack sounds like a pretty good one.  I've never played with those, but at least then you aren't blowing budget on a practice amp that you aren't likely to have much use for when jamming, gigging or recording.  It would probably give you a good assortment of sounds to work with for starting out, and still be useful enough at gigs later.

If you wanted something smaller and less expensive, something like the Vox amplug series might work, and they hold up pretty well to the typical use and abuse.

But get something to start with and start playing.  Learning to play well enough to get the sounds you want is likely to take more time and work than finding gear will.