Luxury sheets and blankets

Brooklinen, hands down the most comfortable sheets I have ever owned (and per the second part of your question, definitely receive my fair share of compliments). It also helps you can get a great set for under a couple hundred bucks

High cotton thread count

Go for long fibre cotton or linen with a TC>300 and you'll be fine. I prefer Sateen (summer) or Percale (winter) weave.

It all depends on your budget.

I second the Brooklinen comment. Reasonable price and very good quality.

Other high quality stuff:
Frette

If you really are a bedding connoisseur and want to throw money around:
E Braun & Co.

I would say Brooklinen is probably your best bet for quality + price.

My friends and I recently went on an expedition to the arctic and we clubbed about 85 baby seals as a group.

The softest sheets you will ever sleep in, are the ones that you club yourself.

(--This is obviously a joke--)

As long as there's no puke on mine I tend to get compliments

I like BAMPURE bamboo sheets because this is 100 % organic bamboo with the approval of OEKOTEX. 

We have both Frette and Sferra. We have Sferra 45 Giza sateen sheets and they are heavenly. We got them because my wife didn't love the Frette percale sheets we had. Obviously, there is huge element of personal preference (sateen is softer, especially out of the box, but warmer) but also, you have to realize that luxury linen, but especially percale, needs to be broken in (ie. slept in for a few month and washed a couple of time). Duvet though, I'm not sure you really need to go luxury. There a some outdoor brands / stores that do duvets (Feathered Friends, L.L. Bean, etc) and you 95%+ of the quality for a fraction of the price. We have both Feathered Friends and Frette comforters and they are so similar that I can't remember which one is at the cottage and which is in the city and the Frette was 3x the cost. 

Check out Parachute, their stuff is amazing and has gotten love from the ladies

Am a very particular gal and can verify Brooklinen is second to none. The cotton percale sheets feel like luxury hotel sheets, they don't start out stiff or crunchy like old fashioned percale sheets, and only get better after washing. Worth the extra $$ to get the sheets, pillow cases, duvets, everything. If you're a hot sleeper (or sleep with a hot sleeper), avoid anything high threadcount, sateen or satin, microfiber, or god forbid jersey knit; this is where the cotton percale sheets absolutely shine

The lady insisted on some pricey brooklinen sheets etc and I gotta say I am very happy with the purchase.That thread count and texture makes a huge difference

Is Bed Bath & Beyond considered a non-target place to get bedding?