Would Appreciate Advice Before I Buy

Greetings and thanks in advance for any and all assistance. I am re-entering the vinyl world in my 60s, now that I have enough time to give to that approach and a little bit of money to spend on components that will help me to enjoy the music I like.

I am only wanting to spend in the neighborhood of $2,000 - $4,000. I realize that's a relatively small outlay, but I also gather that there are good options at almost every price point. Here is what I am contemplating - I would welcome comments. Am I missing something? Will these components "play well" together?

• Schiit Ragnarok-2 integrated amplifier (fully-loaded)
  
• Pro-Ject Debut Carbon EVO turntable 
  
• Klipsch RP-600M speakers
• Bose Quiet Comfort headphones (already own these and would use if I can)
  

I like a variety of music styles: classical, pop/rock, big band, jazz, a little blues and other. I am not a terribly demanding listener, but I think I can hear the difference between great sound and mediocre sound. My room is a currently open large rectangular "bonus room" upstairs in a new home. I can adapt (sub-divide, other) that room over time to improve sonics.

My first vinyl purchase is a set of the Franklin Mint "Greatest Jazz Recordings..." in, well, mint condition that I was able to get very inexpensively at an estate sale this past week. I will probably start picking up some of the re-issued Elvis Costello soon as well. 

What do you think? Thanks again.

David