Help me to build my first stereo system

Off the wall answer: Get a good sound bar for your TV until you get enough budget. Edit: Or start anywhere and enjoy, you'll know where to go after that.

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.