Newbie to the awesome audiophile world

All pretty good discussion, but at the end of the day, for $1,000 it will come down to a pretty short list of integrated amps. Mine would include:

1) NAD 368 - 80WPC, much more peak, modular upgradeability, decent phono stage, lots of awards
2) Marantz PM7000N 60WPC, Streamer, Phono, Bluetooth, WiFi, Alexa, Google Home, high build quality, high sound quality
3) Peachtree decco 125 SKY  120WPC, Small footprint, big value, Good DAC, phono stages, great streaming app, best-in-class remote. Power if you need it.
4) Arcam SA-20 80WPC British, killer DAC, looks 'high-end'
5) Rotel A12 60WPC Good reputation, good flexibility
6) Rega Brio, 50WPC, because the British like 'pace & rhythm' whatever that is, and supposedly the Brio has it.  

Sorry Millercarbon. Crazy to spend 25% of a $2000 budget on wire. Infinitely better spent on active components at this level where another $500 can buy you big improvements.

Said the guy who has never been paid to actually put together a system on a $2k budget. Easy to imagine. Different to do. I did it. Was paid for it. By a customer who told me he has lots of friends with far more expensive systems who won't believe his cost so little. Beside himself with pleasure, he is. Because the fact of the matter is $500 will buy way more performance in wire than you can ever get with a $500 component upgrade. Admittedly this is a fact you can only know by actually doing. Until then you can make up all the imaginary facts you desire. So dream on. Dream on.... 

Already quite a bit of good suggestions here! I am giving the +1 especially to @cpdkee and @panzrwagn (are you driving a Hummer??) emphasizing good amplification.

The speakers you are eyeing seem both to be decently sensitive, obviously the Kef more so. Like @krameshmurthy, I also have a PS Audio Sprout 100, which has been driving successfully (to my ears and listening habits at least) even less sensitive speakers with the Totem Rainmakers, and currently the Rega RX3's. I happen to also own the Peachtree Nova 300 you mentioned, which I have been very happy with and can definitely recommend, especially given it’s vast feature set. That one has driven Amphion Argon 2’s and currently Anthony Gallo Reference 3.1 (which btw I have seen sell on eBay used as low as $1200, which is crazy) - but unless Peachtree prices have dropped dramatically, the 300 might eat up too much of your budget.

I personally enjoy watching a few youtube reviewers that went through the exercise of putting together systems for a similar budget as yours or have great advice on how to go about the process, how to allocate your budget and what advice to tune out. These guys might give you some additional ideas:

Steve Guttenberg’s equipment advice:
1.) https://www.youtube.com/watch?v=0Y3SUdc7J2M&list=PLKlGuF--sgHus5VYQ-pUvEEyFh2-_k1SY&index=4
2.) https://www.youtube.com/watch?v=Fdb8wLd73Tg

Sean / Zerofidelity Really great thoughts from someone who knows well the current market and this video seems largely geared towards people with exactly your type of budget ($1500-2000) “How to manage your Hi-Fi budget! Advice For Beginner Audiophiles.”
https://www.youtube.com/watch?v=87zFhwqWXXI&list=PL3XRie2Nc6cgv--IgpXPjYWLEJJcot8S1&index=13

And not to forget John Darko, addressing beginner audiophiles on what to IGNORE (until later) before getting too caught up in some of the advice that is overshooting the goal as outlined by you:
https://www.youtube.com/watch?v=GUZhtQheELg

MC - maybe good for you to watch as well:

https://www.youtube.com/watch?v=GUZhtQheELg

Welcome!

I suggest that you go around the retailers and listen, listen, listen. Visit a high end store too - they may just treat you a whole lot better than the chain stores - at least, that's my experience. And they often have used/demo equipment too. Main thing is to be exposed to various sounds. Planar speakers are very different from box speakers. Vinyl is very different from digital. Etc. Etc.

You may find that you only need to spend half your budget to get what you want. Then again, you may become like most of us here ...

Just don't get conned into spending a lot for cables, a HUGE profit centre for retailers. Sound of cabling is almost uncorrelated to cost, and what you spend on cabling can't be spent on speakers.