Help me to build my first stereo system

Welcome to the machine, and congrats (condolences) on the upcoming nuptials. I’d recommend this system. The amp is a The Absolute Sound product of the year and also has a nice internal DAC in case you wanna get into streaming at some point, which you absolutely should. The turntable has a better tonearm than the one you chose and also allows for important vertical tracking angle (VTA) adjustment, and I think just flat out looks better. The speakers are excellent Wharfedale speakers with a walnut finish that will nicely match the turntable (fyi, wives love stuff like that). Total bill — $1500 plus tax.
https://www.usaudiomart.com/details/649956133-nuprime-ida-8-ultra-low-noise-class-ad-integrated-amplifier-with-dac-silver/

https://www.crutchfield.com/p_336D120WLN/Wharfedale-Diamond-12-0-Walnut.html

https://drop.com/buy/drop-audio-technica-carbon-vta-turntable

If you’re leery of buying the amp listed above used (although it’s got low hours and should be perfectly fine), this Yamaha would make a good substitute and has a phono input that may or may not be better than the phono preamp in the turntable, but you can compare and choose — I’d go with the NuPrime amp above if I was you as it probably sounds better and likely has a better DAC. Hope this helps, and best of luck.

https://www.accessories4less.com/make-a-store/item/yamas801bl-rb/yamaha-a-s801-2-ch-x-100-watts-integrated-amplifier-w/dac-black/1.html

It's as subjective as picking a favorite color, and your speaker selection should take your room into consideration, so take most of our specific favorite recommendations with that in mind.  You really need to satisfy you. 

I'd spend most of my time and budget finding a pair of speakers you love that will work well in your room, then focus on an amplifier that will drive them.  Add music source as money allows.  

Buying good used gear can lead to some great bargains.  

BTW, the reason I recommended the Wharfedale speakers over the Klipsch is that they’re a straight-down-the-fairway, very good speaker that’s well balanced and won’t offend you in any way.  The Klipsch, on the other hand, can sound bright and become fatiguing with extended listening depending on the system.  A good system is all about balance, which is why I recommended the system I did.  I think the system you mentioned could potentially sound bright and fatiguing, but that’s just an educated guess.  Just my $0.02 FWIW. 

Can’t go wrong with a pair of Vanatoo active speakers ( assuming still available) and table with cart of your choice + Rega Phono mini phono preamp. I own and can vouch for both.  Rega, Project or Cambridge would be good turntable choices were it me  

@augjonas 

With your budget, why are you looking for a turntable?

Vinyl is expensive to do well and it expensive to build a library of music.

You have to search for and then buy everything you can listen to.

Why not bypass vinyl and go directly to digital. Buying a streamer and a subscription to Tidal or Qobuz will allow you to have millions of songs at your fingertips.