What I personally use...
Interface: Audient iD24 MKII
Cables: Mogami Gold XLRs
Headphones: MOONDROP x Crinacle Blessing2:Dusk (IEMs) or Beyerdynamic DT 770 Pro
Microphones: Shure SM7B, AKG C414 XLII, Earthworks SR117, Microphone Parts V69 FET (DIY using MXL V69 body), Audio Technica AT2020 (Overhauled with Microphone Parts Upgrade Kit)
What I would suggest in your price range (like if I were to start over and have that budget)...
Interface: Audient iD14 MKII (~$350) (note: NOT iD4) or Presonus Quantum HD 2 (~$400)
Headphones: I love my IEMs for comfort, but I also do love my BD DT770 Pro @ 80ohms (~$150-$200)
Microphones: If I were to start over and choose one at this price range, I'd pick a handheld condenser mic: JTS NX-8.8, Rode M2, Earthworks SR117 (I got mine for ~$175), or Lewitt MTP 350CM (choose whatever is cheapest in your country?). I chose handheld condenser based on what I was recommended and experienced from that recommendation. Handheld condensers has more open-ness (better range) than most dynamic mics. Since a lot of them are built for stage use, they're good at blocking out background noise as well (especially with tighter patterns like Supercardioid).
I didn't suggest any large diaphragm condensers because your room is not treated and they can get very expensive very fast. There are so many options. I prefer DIY if you can solder, the main mic i use is the converted V69.
If you are insistent on having a large-diapgragm condenser, I'd suggest sticking with Lewitt as a brand for <$1k budget; I also heard great things of the Warm Audio WA47 (~$1000) from an audio engineer (Lintu) if you want to save up for that later on like next year or two.
Cable: Mogami Gold unless you learn to solder and create your own.
Please understand that these are personal preferences. Always do extensive research before locking in on a specific product. Buy from somewhere with good warranty or somewhere where you can return it. Be wary of counterfeit microphones (popular ones like Neumann, Shure, etc have counterfeits) if buying from FB Marketplace or Ebay.
There are tons of videos on YT on how to make your room quieter. Take time to understand how sound is reflected before investing in any room treatment. There's no shame in singing under a blanket or having a life-size teddybear behind you.