I always design in 2x files. If I worked in a 1x file, it wouldn't look good on my 2x Retina display (it would be pixelated). Even if you don't have a 2x display now, you will eventually. Just like all displays went from B&W to color, they will eventually all become 2x. At some point we won't have to worry about 1x anymore. So why would you want all your files to be at 1x?
Plus if you're using Adobe Generator, exporting 1x and 2x aren't a problem when scaling a 2x file down to 1x. The same can't be said for designing in 1x files. Adobe Generator has a bug with JPEG based Smart Objects so it can't enlarge them to 2x properly. Just another reason to work at 2x.
Working at 1x or 2x both have pros and cons. But I think working at 2x has fewer problems and is a more modern workflow. Fewer people use it because they don't really know all of Photoshop's features and are so used to working at 1x, but I believe designing at 2x is absolutely the way to go.
You do want to use as much vector art as possible, in part because it should later be exported as SVG for use in your webpages. Sadly Photoshop often can't export SVG properly (if it's a vector smart object it can't export properly) so you'll end up needing to export the SVG from Illustrator.
As a side note, designing in Sketch or Adobe XD avoids many of the headaches of designing in Photoshop. XD isn't quite ready for prime time for most people, but it's getting closer with each release.
P.S. I know a lot about this topic because I'm an Adobe Certified Instructor in Photoshop with many years of experience with all sorts of web design apps (such as Photoshop, Illustrator, ImageReady, Fireworks, Sketch, and Adobe XD). I wrote Noble Desktop's Photoshop for Web Design & UI Training Book which teaches these types of concepts. In there I cover designing at 1x and 2x. We should have a CC 2017 version of the book on our site in the coming weeks, although the CC 2015 version will still mostly work in CC 2017. The biggest change is the File > New dialog.