Help me to build my first stereo system

I was under similar budget a little while back and ended up getting a Rega Brio integrated for $300, Tekton Lore speakers for $500,  Schiit Audio dac for $200 running through an older NAD dvd/cd player and I’m extremely pleased in the result  for money spent.   You mentioned a turn table and I did not go that route.   However I think you can certainly put together a nice set up within you budget with some research and advice from the experts on the forum.

@augjonas Give the stuff a try! And of course -- remember that speaker position is what’ll make the magic happen. Away from the back wall. Up on stands. The two speakers and you in a triangle.

Find a good local hi-fi shop, of the independent, "high-end" variety. Even if you have to travel several hundred miles. Make it an overnight trip. If you provide your approximate location, perhaps those in your vacinity can suggest a dealer or two.

You can't expect perfect (and imperfect ;-) strangers to know what you find appealing in hi-fi gear. Helping you find a musically satisfying system is the job of a professional retailer. His profit margin is built into the price of every piece of hi-fi gear on the market.

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