I started on electric. 

When I started playing acoustic, there were a few things different that I had to get used to. 

The weight and balance are different.  Electrics tend to be heavier, and that can lead to supporting the violin's neck more with your thumb than you should.  Also, hand movements that wouldn't move the electric much may move an acoustic more, and that can throw off your fingering a bit.

Bowing is a little different, or maybe it would be more proper to say that the sort of sound you may get from the same pressure and speed of bowing you do on one can sound quite different than the other.

You also have to remember the overall sound is a bit different.  If you try to learn techniques from something like a recording or video of an acoustic but you are playing electric, you may have to listen a bit closer to tell if you are getting it right.

But really, those are things you get used to pretty quickly, and both are great fun.  I play both and switch back and forth between then quite a bit.  The advantages of electrics being very quiet with the headphones (or just not turned on or not plugged into an amp) allows practice at pretty much any time, and I'd say that outweighs any disadvantage "solid body" electrics have.

And like I usually tell folks, if you can manage to have both, that's the best option in my opinion.  I have both, and like playing both of them.  (Well, not at once, obviously..LOL)

Si I agree with Fiddlerman, hat it won't hurt you, but you'll have to get used to playing acoustic, if you decide to do so at a later point.  Most of what you learn on either will work on the other as well.

Electric violin frequencies aren't a problem with a guitar amp.  As Fiddlerman mentioned, electric violin and electric guitar have a very similar range.  Guitar amps do have some tone shaping that is intended to optimize guitar sound, but that varies from maker to maker and it is just a matter of finding a brand of amp you like the sound of or getting the tone controls set in a way you like.

Semi-acoustic violins (an acoustic with a pickup) will not play any quieter than a regular acoustic.  The point of putting a pickup on them is so they can be amplified to play louder.  Or maybe if one wants to try using effects or recording directly from the instrument instead of setting up a microphone.  Amplified acoustic violins are only "the best of both worlds" in that they allow the use of effects, direct recording or amplifying the violin where natural volume just won't be enough power.  "Solid-body" electric violins are sometimes sold as "silent violins" because they are much quieter if used unamplified or with headphones. 

My electric, when played without plugging it into an amplifier, can be maybe as loud as a person speaking in a quiet voice.  Nobody would be likely to notice any difference if I wear the headphones or not, but they are nice when you want to be able to hear yourself over background noise, like someone watching TV or whatever.  Plug it into an amplifier and it can go as loud as the amp can go, which can obviously be very loud if that's what you wanted.

I don't use mutes.  But they work by damping/absorbing sound from the bridge.  On an acoustic violin, that keeps sound from getting to the body or "sound box" of the violin, so it makes it quieter.  However, with an amplified acoustic, it would also keep sound from getting to the pickup.  I can't think of any situation offhand where that would be an advantage, unless maybe there was something about the tone of the instrument played with a mute that you wanted maybe for recording or something.  It definitely wouldn't make a semi-acoustic violin so it makes no sound except what comes out of the amp, though.  For that matter, solid body electric violins also make some sound when you play them even with no amp, it is just much quieter.  A bit louder than an electric guitar played with no amp, but not a lot.

Now, to address a comment Stuey75 made.. Maybe your house is set up differently than mine, but if people are asleep and I play the acoustic violin, it often will wake them up.  Acoustic violins are powerful little instruments, and the sound carries quite a ways.  If people are asleep, I play my electric.  If I don't have it plugged into my (guitar) amplifier, it is quiet enough that it doesn't disturb anybody. 

Most of the e-violins I've seen for sale lately have a headphone jack.  You might want to check the product description to be sure, though.  In the unlikely event that you find one you really like that doesn't have a specific headphone jack, there are inexpensive headphone amps as well as amplified headphones on the market.