Some feel music is the end all be all and will say go with an Integrated amp first. And that path is fine enough.
Given you want to improve upon the home entertainment experience as you noted the nice TV and blue ray player I’d opt for a different theme or plan.
just starting out I have always gone with a multichannel receiver. always. But, that's just me. Were I doing it all over again, I’d try hard to get one of the top tier receivers and having had a few, Onkyo is a very solid option with very good support, in or out of warranty. Well built and very reliable. Sony is another decent choice. My Onkyo has out lasted my Sony though. Performances are pretty much a toss up.
Ensure whichever way, the multi ch reciver is capable enough for 4K video, either HDR or now, Dolby Vision, if possible. Or look for HDMI 2.0 on the video side. I’d never buy one with less than 110 – 120 wpc either. Mo’ is better.
having a multi ch receiver enables one to add many things, as you are able. or, when you are able.
Speakers were first. I’d opt in for a 4.0 aray. Then likely add a sub. HT just ain’t HT without a sub. I can live without a center channel long before I can do without a sub woofer. Subs are a must for HT.
Then, I’d upgrade the mains. Usually moving them to the surrounds. If possible.
Once I had all four ch, and a sub better off, I’d add an amp for the mains. Either a multi ch amp or a nice two ch amp. Use the reciver to do the processing and run the surrounds.
Then its off to upgrade heaven. The world is your play pen. Where ever, what ever, when ever you have the dough for the upgrades.
Ultimately, you wind up with a bed room outfit and a very nice main HT rig. If you don’t have to sell off stuff to do your upgrades everytime.
I’ve even bought older speakers and sent them back to their maker for upgrades, essentially then having brand new speakers for much less than buying brand new units..
This is the idea for all of us. Many even enjoy the process. I’m more of a “Are we there yet sort though” and don’t care a ton for the crap in the interim. But yeah, even still, it is fun when new stuff comes into the house and you find out exactly what is what by ‘experiencing your plan’.
Either way, getting a sub as soon as possible will really add to the AV experience.
Be well, J