Help picking a mid-level camera?

I'm looking for a digital camera I can purchase on Amazon (it's a gift card) for at or below $150. In order of most important:
#1 price - if I HAVE to I could save up to a limit of $375…$100-$200 is better though
#2 compatibility w/a shutter remote (would appreciate if you know a good one too)
#3 compatible w/most tripods (I already have 2)
#4 anti-shake/stabilizer
#5 resolution/quality of still image
#6 SIGNIFICANT superiority to smartphones & tablets
#7 BONUS video quality - including ability to pick up sound from a few feet away

I need a nonbiased person ideally someone who can tell me the REAL difference between "new", "used", & "refurbished"… I've always gone for brands I recognized & only brand new but am trying to keep an open mind

I got a chance to see the Nikon S1 being used and was impressed tho don't know if it will fulfill my remote shutter accessory requirement (I don't expect is to be included but MUST be compatible) but is DOES have the option to switch lenses like my old one, the only other downside I could see is, according to this Amazon listing for this:
Nikon 1 S1 10.1MP Red Digital Camera with 11-27.5mm Lens (Certified Refurbished) https://www.amazon.com/...00THM31D0/
which an identical (though refurbished) cam to the mom's cam is that it is only 10 megapixels and I was hoping for at least 12 if not even as high as 16.

1. Price under $375. Check.
2. Remote Optional and available. Check.
3. Compatible with all tripods. Check.
4. Shake Reduction. Check.
5. Picture quality. Depends on your skill.
6. Video/sound quality. Depends on your skill.

http://www.bhphotovideo.com/...black.html

New - Camera came from a sealed box.
Used - Camera has gone out of the box.
Refurbished - Camera went out of the store but came back due to factory defect then was returned to the factory for repairs then back to the store shelf and sold with a marked down priced. Great if repairs are actually done by the factory. Those done by unauthorized technicians, avoid.

Check out keh

All these here meet your requirements: https://www.keh.com/search/list?n=128&sort_by=priceMax-asc&category%5B%5D=Complete+Cameras&mfg%5B%5D=Canon&mfg%5B%5D=Fuji&mfg%5B%5D=Olympus&mfg%5B%5D=Panasonic&mfg%5B%5D=Pentax&mfg%5B%5D=Sony&stb%5B%5D=239&stb%5B%5D=240&fmt%5B%5D=211&fmt%5B%5D=212&price_min=0&price_max=375

New means in a sealed box
Used means somebody used it, box has been opened
Refurbished means it has had an overhaul/service/repair