Some thoughts:
Sources - this is a whole area of its own, independent from the audio system.
Vinyl will be the biggest hurdle here. Vinyl just has space and equipment requirements that you can't get away from, and it does not rip well to digital, plus that sort of destroys the whole point of vinyl. You need a turntable, (tone arm and cartridge will be included for most entry turntables, otherwise you need to add those as well) and phono stage/phono preamp. There are entry level products that have that built in.
The CDs I'd advise ripping to FLAC (lossless) and storing on a NAS feeding a digital media server, that server will also be your connection to Amazon Prime and to Tidal or Roon in the future if you really get into high rez sources. The NAS you can also use on your home network to back up computer files, feed a Plex server so you can download TV shows/movies to watch on smart TV, etc. Some streamers have a drive built in, but your collection will likely be too large for the drive, but to keep it simple, you can just get an external USB HDD and most of the streamers can directly connect USB. Going to a NAS like a Qnap gets you more space but also RAID redundancy, so you don't lose everything if one drive fails.
Be aware ripping the CDs will be a long, time-consuming process, and it pays to research the CD database software so it does all the naming/tagging automatically. There used to be some companies that you could pay to rip it all for you, you send them your disks, they send you back the files. But that's the better future-proof solution, and frees up your future physical storage space as well as your need to keep a CD player. That said, if you really want a CD player, the obsolescence of CD has killed resale values of top-end CD equipment and you can build what used to be a 5-digit dream system for low thousands.
Outside thought, unless your CD collection is really esoteric, take a look at the Roon/Tidal catalogs. You might find they already have digital high-rez versions of all your CDs, in which case you might just pay for a subscription and stream it all vs the time/hassle of ripping your own stuff and needing a drive to store it.
You need to think about where you want to be on the convenience vs sound quality scale. You can have both, but not cheap. And you also need to consider what audiophiles refer to as WAF, Wife Approval Factor. Can the system be visible? Can it occupy a bunch of space? Does it have to look nice in addition to sounding nice?
Even a few Sonos speakers gets you into the thousands that you are trying to avoid. Sonos is nice for convenience, but once you start talking about multiple units/surround sound or multiple rooms/zones, the cost adds up.
Room actually seems pretty good, good size, open sides, carpet, those make it easier than a small reflective room. But the size and the openness would push me towards floorstanding speakers over bookshelves and over sound bar type products.
If you lean simplicity, consider active speakers, which means amplification is built in, so you don't need a preamp and amp to drive them. Some of these have Bluetooth capability built-in, in which case you could just run audio from your PC or phone. That's how a Sonos setup works. At minimum I'd consider an integrated amp with Bluetooth or streaming ability. That keeps you to one box + speakers.
System concepts, from less to more. Generally correlating to performance but not really. But correlating to simple/cheap/performance, pick any two. And definitely in order of WAF:
Source (phone/PC/streamer/turntable)-->active speaker with BT input (Sonos fits this, KEF has a few products at higher prices, this is a small niche product so your price is higher and your selection is lower)
Source-->integrated BT receiver-->speakers
Source-->BT streamer-->integrated amplfier-->speakers
Source-->BT streamer-->preamp-->amp-->speakers