Hi rawrgs.

Within the budget range you are talking about, you have more than a few options.  

I don't know as anyone can tell you for certain what you should get.  What you'll hear will tend more to what we would get, given the same budget.  So there will be some ideas to consider, and to think over as you are deciding what you actually will get.

Ok, so you feel you'd prefer electric.  In some ways, this particular forum (as well as most other violin forums) has a bit of bias towards acoustic violins.  I play both electric and acoustic, so I am going to suggest that even if you mostly want to play electric, consider spending part of your budget on at least a modest acoustic.  It doesn't have to be a great one, and as I recall, Fiddlerman carries a Cecilio acoustic that runs around 100$ that he feels is a good enough instrument to get a beginner started.  I feel there are a number of reasons for having both electric and acoustic. 

First off, some sounds/techniques are just easier to get on one than the other.  But once you can get the sound on either, it is usually pretty easy to get on the other as well.  Acoustics are great because they are so portable and they have the "traditional violin sound" for when you want it.  Everything you need is right there in the case.  Electrics are also great, since you can play them any time day or night (they are very quiet when used with headphones or just not plugged into an amplifier) and you can try them with different effects made for instruments like electric guitar.  

But if you have both, then you have all the options.  To me, it is also more fun.  Playing on both, I feel I may have learned some things a bit easier/faster, if only because I just end up playing more. 

For electric, you also need to consider an amp.  The bad news on that is that amps can be expensive and a lot of gear to have to lug around.  But the good news if that there are quite a few nice amps even around 100$ that can do a good job.  If I was starting out, I'd look at something like a Fender Mustang or Frontman.  Get one of the models with reverb/delay built in, and that have both drive and gain controls, and you will have quite a lot to work with so far as things you can do with your electric sound.  Even before you get around to trying effects pedals and such.

Doing a quick look on the net, something like this

It would be enough power for practice, jam sessions, and even some gigs.  10 inch speaker will have a reasonably good bit of low end when you need it, and there's really nothing on that amp that wouldn't be quite useful for even a beginning player.  It's a decent name brand with a fairly solid rep, and not likely that even if you buy something bigger and nicer someday that you'd ever want to just throw it away.  Useful enough.

Okay, so that's about $200 of your budget right there.  I'd say lop off another $100 for some nice strings, good rosin, a decent "patch cord" to connect the electric to the amp and maybe an electronic tuner. 

Okay, so that would bring us down to about $400 for the electric violin.  There are quite a few electrics in that price range.  On the Fiddleshop that Pierre (Fiddlerman) runs, you could get one of the "Plug&Play" ones for that.  You might find something you like even better if you shop around a bit.  But another option (the one I would probably do myself) would be to buy one of the less expensive CEVN models (just going with what is available on Fiddleshop, for the sake of argument).  There are people here that play them, and at least one experienced player here has mentioned that the balance is good and thy play pretty nice. 

That would leave you with about $250 that you can set aside and spend on things like a nicer bow or some effects or if you need replacement strings or want to try a different set of strings or whatever.  But it would be basically for those things that you don't know you need until you actually get playing and then decide you want.

So that is what I would do.  It won't be the same as what other people here would do, and probably not exactly what you'll end up doing, but maybe there's an idea or two that you hadn't considered that may be of use to you.

And welcome!  Violin is a very fun and cool instrument and this is a very good online community.  However you decide to spend your money, I think you're in for a lot of fun and for some memorable good times here.  Pleased to meet ya!