Need help choosing my first amp for my first speakers

Congrats on some great speakers!  That’s the good news.  The less good news is at 83-86dB sensitivity and 4 Ohm nominal impedance you’d want an amp that puts out at least 100 Watts per channel into 8 Ohms and basically double that into 4 Ohms.  Suffice it to say the Wiim Amp underpowered for the task.  In a perfect world you’d save for a more powerful amp, but I understand you really wanna at least hear the speakers with something.  The Wiim will probably work just to get some sound going, but you should avoid turning it up loud because the amp could produce clipping distortion that will at the least won’t sound good and at worst could damage your nice speakers.  In terms of cables, you could start with these as they’ve gotten some nice feedback here for the price and like the Wiim will at least let you get started.  You’ll probably also need an Ethernet cable to run from your router to the Wiim, and maybe someone else here will chime in with a cheap but decent option for that as well.
https://www.amazon.com/dp/B06ZZ5HCTM?ref=ppx_yo2ov_dt_b_product_details&amp=undefined&th=1

Positioning will be critical with these speakers, and these guys don’t like to be near walls to produce the imaging/soundstage magic they’re capable of so I hope you have the space/flexibility for that.  I’d have the backs of the speakers at least around four feet from the front wall and a similar distance from the side walls, and I think the designer prefers no toe in but you should check that.  Ok, hope this is a little helpful, and best of luck pulling this together.

Thank you so much for your detailed response @soix. Really helps me a lot! One question, is there a reason why you are calculating for 8 ohms when the spec is Nom. impedance: 4 ohms? And would the calculation be that the amp needs to supply 200 watts per channel at 4 ohms (This speaker)?

There is an AG add from Listen up Audio for a Cambridge Audio 851 integrated amplifier at $650 with free shipping.  You may want to check this out. A review from Steriophile is available online. Use the Wiim as a source only. 

Take care of those Speakers, don't drive the amp too hard.

One question, is there a reason why you are calculating for 8 ohms when the spec is Nom. impedance: 4 ohms?

Personally I’d want at least 200Wpc at 4 Ohms to handle the W5’s impedance dip(s), and to get that you’re gonna need to look at amps that are at least 100Wpc @ 8 Ohms as that’s the number you’ll more readily see without having to dig deeper into the specs. 
 

Here’s another all-in-one idea that if you can stretch for would likely serve you better than the Wiim Amp as it likely has a much better DAC and power supply and probably sounds better overall.  The USB input is limited to 24/96 but that should be more than fine for now.  Just another option FWIW.

https://www.usaudiomart.com/details/649987921-bel-canto-c5i-integrated-amplifier/

How big is your room, how loud do you want to play?

Those should have some excellent midrange clarity and sound stage, but aren’t likely to "rock the house" as-is....I’d want to put a nice tube amp on them to get the most from what they do best, then run a well matched active subwoofer to help where they don’t excel. .I’d give you’re current amp a whirl and see how it goes, but would likely consider the subwoofer even if I kept the amp. Your room will definitely come into the equation though.