16' x 13' is a decent size space which gives you a lot of options.

Standmount or floorstander doesn't really matter, that configuration isn't really any indicator of what will work or not in any given space.

Most important thing with the room, especially since you want relaxed and non-fatiguing sound is plenty of soft furnishings. If you don't want wall to wall carpet you should aim to cover at least 80 percent of the floor with thick rugs. Likewise, curtains on the windows and some fairly chunky well padded fabric covered seating. This will all damp down reflections that cause glare and fatigue.

For loudspeakers, and I'm guessing you want to buy new, check out Wharfedale Super Linton https://www.wharfedale.co.uk/products/super-linton

Well balanced speaker that tends towards sounding 'warm and relaxed', so easy to listen to, but will still give high fidelity reproduction.

Not saying buy that specific speaker but it's one to use as a benchmark when comparing to others.

Most modern amplifiers will have no problem driving it. There's multiple options there, I'd suggest power output of at least 50 watts which you probably won't need as much but better to have it and not need it.

Look at amplifiers with the inputs you're going to need for your sources, and that have the aesthetics that you like. If you like old school looks the modern Yamaha amplifiers are competent and not over-priced. Again, just a benchmark.

I don't personally use streaming so I'm reluctant to make any recommendations there. Most members here do though, so I'm sure someone will chip in on that with some advice.