To hit all your wants at your budget, I'd probably direct you toward a modeling amp of some type: Fender Mustang, Marshall Code, or one of the Line 6 Spider amps.
I would look at a Marshall Code 50. $250. 12" speaker. Tons of available amp profile and effects. 3.5mm aux in and a headphone out that mutes the amp.
Unless you're buying a tube amp, get wattage out of your head. Wattage matters in a tube amp because your tone is largely depended on how hard you're stressing the amplifier. To get an Angus Young AC/DC sound out of a 100 watt Marshall Super Lead, you're playing it at arena volume. To do something similar on a small 15 watt combo amp, it's at a much more tolerable home-friendly volume. Not that I'm comparing a 100W head to a 15W combo, but to get substantial breakup on a high watt amp, it comes with lots of volume. No so with a lower wattage amp.
Tone on a modeling amp is shaped using DSP and can be done at any volume. So you'll get your AC/DC sound no matter what the volume is. Tone is not depending on how hard you're pushing a gain or power stage.
Bluetooth? What do you want to do with it? Connect the guitar to the amp? Yes, there are wireless systems that use a transmitter and receiver for wireless guitar connection. They're not in your budget and frankly not necessary for home playing.
Mic input? Microphones don't go into guitar amps. That's what PA systems are for.
On a personal note... I hate modeling amps. I own a Fender Mustang. I have never been satisfied with the tone. Again, this is personal. Lots of players love them. I don't. I would stretch my budget and buy a tube amp. $380 will net you a Fender Super Champ X2 (which has an extensive number of preset tone controls), $420 will get a Fender Pro Junior III (which has a great clean tone), and $450 will buy a Fender Bassbreaker 007 (which, to my ears, sounds much like an early Marshall... I happen to own one of it's big brothers, the Bassbreaker 15). If you want to shape your tone or change effects, add pedals. I've found this to be much more satisfying... but again, that's just me.
Lastly... get to a store. Plug in. Play the amps you're considering.
