To get the strong decrease in volume that's possible with some electrics, you have to get a solid-body one. By their nature, those have no tone worth speaking of. Any tone involved in those comes from the electronics. You can affect the tone a little by how you play, but not nearly as much as you can on an acoustic instrument. (@Fiddlerman, you have a better quality electric - if I'm wrong about that, please correct me.)

From everything you say, you want an acoustic, of as good a quality as you can afford. Speaking from experience, don't get one that's cheap and not set up, because you'll lose any money you saved by buying off Amazon or wherever in having a luthier do the work that's needed to turn it into a decent instrument.  I recommend Fiddlerman's stuff, but he's not the only decent, honest shop. Just make sure a professional setup is part of the price.  (I do recommend avoiding Kennedy Violins. I've heard several stories of bad experiences with them.)

Then, sans mute, play it anyway.  You're probably envisioning your neighbors getting together with pitchforks and torches and storming your apartment. They won't do that. Or laying in a puddle outside your doorstep, sobbing "Please, stop!". They won't do that, either.  Far more likely (once you get a few songs under your belt) is they'll run into you in the parking lot (or maybe even get brave enough to knock on your door) and ask "Could I come over to listen sometime? It's so pretty, and I'd love to hear it without the walls in the way."

However, if that takes far more courage than you can drum up (I won't give up on encouraging you to move past the fear, but that's for another day), there's another sound option to the mute. It's a fair amount of work, but it can be done medium cheaply. Build you a sound booth.

The basic idea is to surround yourself with sound-deadening material. Fortunately, lots of stuff that can be had pretty cheaply (much of it free) will deaden sound fairly well. The main idea to remember is to reflect the sound towards other things that absorb sound, not towards things that reflect or transmit it. Smooth things are your enemy for deadening sound.  Drapes, towels, egg cartons (the bumpy part) all work quite well. Just make sure you don't smooth them out. The pleats in drapes make them much more effective at absorbing sound. Do similar things with towels. (The fuzz on the towels is good for high-pitched sounds.)

Build a cage large enough for you to stand or sit in (your preference) with room to bow. If there were one direction you were ok with sound going out, you could leave one side open and put the music there, but I'm assuming you don't want any sound getting out (lest there be pitchforks ) so you'll need enough room for the music, too. Just body heat will make it get warm in there pretty quick (all this stuff makes pretty good heat insulation, too), so use LED lights - they'll put out the least heat. (Unless you want to memorize all the music first and play in the dark. That will cut down the size requirements, too. )

If you're not crafty with furniture-like projects, you may want to get a friend to help. You have two options for building this. Lightweight, which will be much easier to move around (and move from apartment to apartment), but which will put limits on what you can use (egg cartons will be about it), or heavyweight (2x4s), which will let you hang pretty much anything you want on it, in multiple layers, but will require some good design work or you'll never be able to move it anywhere else. Since you're really, really paranoid about sound getting out, I'd recommend the stouter version.

Fair warning - all instruments (including voices) sound somewhat dead in one of these. They use fancy versions of them (they're officially called anechoic chambers, I believe) for recording, when they want the sound coming from the instrument and absolutely nothing else.  However, while you'll lose the echoes from the walls, it will NOT distort the sound coming from the instrument the way a mute will.

Or take the easy way out and go through the week of hell playing it unprotected and dreading pitchforks, and when your neighbors DON'T try to kill you, realize it's not actually all that bad if they hear you and start enjoying it.   But get an acoustic either way. From everything you've said, you're not going to be at all happy with a solid-body electric.

Talk to teachers - they frequently rent violins themselves, and are at least likelier than most to know what decent ones are available and from who.

And congratulations on your choice of options.