Ok that makes sense. I just thought it might be a housekeeping thing.
So I’d do the following then;
Do what @Dag_Otto suggests and add
Your cassette player : Free
turntable: $150
CD player $300
If I understand you correctly, you are looking to replace the rich, deep, natural sound of vinyl or CDs played on an old component-based stereo system with the modern weak, tinny, audio experience of compressed audio files streamed through a smart phone’s Bluetooth accessory speakers. 
I just want to say this is a very helpful thread, because I have a similar problem to the OP. While Googling around, I found these links helpful, in case anyone else wants to take a look.
I know you’re kidding here, but there’s nothing weak or tinny with those components I suggested, and nothing compressed with Tidal HiFi (it’s FLAC or better). I’m listening to a very similar system as I write this, and it’s far better than any Bluetooth speaker I have heard.
The exception is the wireless remote speakers, I have not heard them, but based on the OP’s comments, I think they will be fine for him. Yamaha does make bigger wireless speakers, but they would bust the budget here.
Kind of kidding. I’m just recalling from my college years (early 90s) and earlier when the component systems the OP describes were a “big deal”. Of course, the down side is that half your dorm room was occupied by a set of giant tower speakers and subwoofer.
But truth be told, I have a small Harman/Kardon bluetooth speaker that’s about the size of a standard brick and it sounds perfectly fine for blasting tunes from my computer.
The link that I listed above talks about streaming quality as compared to CDs, and the various offerings in hi-res per platform. Basically, hi-res streaming is better than CD quality. For example, it says
The earliest streaming services weren’t high fidelity. They were more like AM radio, but they worked, and they satisfied a music-hungry market. In general, when played through computer speakers or smartphones, the sound was good enough, but if the system were to grow, the quality needed to improve.
There isn’t a strict definition of high fidelity in streaming, but basically it refers to uncompressed music of at least CD quality. Higher than CD quality – termed Hi-res – is defined by The Digital Entertainment Group (in conjunction with the Consumer Electronics Association and The Recording Academy) as the following:
Hi-res audio is: “Lossless audio that is capable of reproducing the full range of sound from recordings that have been mastered from better-than-CD quality music sources.”
Since CDs have a sampling rate of 44.1 kHz and a bit depth of 16-bit, and Hi-res files have a sampling rate ranging between 96 kHz and 192 kHz at 24-bit, the better-than-CD quality spec is the target that the best streaming sources aim for.
Your link also says “The reality is streaming does its best to get to CD quality, but, in general, your music will sound better coming from your own discs or local file (on your computer) playback (like a downloaded high-resolution file that is sitting on your home storage).”
So the answer is “depends”.
As a general rule, the more you spend the more you’ll hear. Go into a stereo shop and audition a $1,000. system, then audition a $5,000 system and you’ll be saying to yourself; gee this is the first time I’ve heard that symbol crash!
Speaking for myself, I was able to put more money into my amplifier because I have no use for a receiver - I have no interest in commercial radio.
Don’t get bogged down with technicalities because with a complete system under say $1,000. it’s not going to matter whether you’re playing (or converting to CD) FLAC files or lossy MP3’s (for example).
Decide on the functions you want your system to perform.
Then my advice would be to go into a stereo shop that has knowledgeable staff. This would typically be a higher end shop but that’s OK, they’ll have cheaper stuff too. Or you can always just pick their brains. Then trust your ears. But remember it will sound different in your home and different whether you have carpeting or hardwood etc. The beauty of less expensive systems is none of the picky stuff that drives audiophiles nuts matters that much. Some people will drop $1000 just on speaker wire & cables. After all, no sense spending 20 grand on a system if you’re going to connect the speakers with lamp cord.
Indeed, thanks to modern high-tech you can have a speaker that is small/compact and sounds good, if that is what you are looking for, but that does not directly translate into inexpensive.
When you read reviews comparing mere CD-quality sound to hi-fi formats like 24-bit/192 kHz PCM or DXD— there is a difference and I’ve heard it myself— they always use a setup where the DAC alone costs around $2000
along with high-quality headphones.
If the streaming service offers hi-fi at the same price that’s great, but in the current scenario CD quality is going to be adequate (we are so spoiled these days!)
There is a paradoxical phenomenon where certain kinds of distortion sound OK or even pleasing to the listener. But they do not mean the kind of distortion produced by tinny, blown-out speakers 
I would be interested in checking that out. My sense is that any stereo system you get from Best Buy will probably be “fine”. But they never sound “great” to me.
Yeah well, just be careful or you could wind up trading in your house & family.
I use floor standing because I found they have a ‘fuller’ sound. A little more on the lower (bass) end. I do have bookshelf speakers upstairs though (mounted on stands).
Both pair are Martin Logan: Motion 40 & Motion 1. Also prefer the efficiency, if that’s the correct word, of ohm output. I believe they’re 4 & 6 ohm, as opposed to typical 8 ohm.
This was my budget. To achieve a really noticable upgrade in sound at this point I’d probably have to spend near double what the Motion 40’s cost, otherwise it would likely be more of a sideways move. There comes a point of diminishing return. So many aspects need to be taken into consideration - not only how much you have to spend. No point cleaning out the account if you live in an apartment with thin walls. Pricey speakers will still sound good at lesser volume, but better with some push behind the volume.
This is intriguing to me - I have a bunch of LPs and cassette tapes still, many of which are pretty obscure stuff that I will never find in another format. (Like choral concerts I sang in, obscure 1990s world music groups, etc.) Did you ever look into some way to digitize the cassettes?
Here’s a tip. Avoid things like equalizers. Spend that on upgrading amplifier & speakers. Good amp/speaker combination doesn’t require sound enhancements. They don’t need bass/treble controls either.
Step-by-step tutorial:
https://manual.audacityteam.org/man/sample_workflow_for_tape_digitization.html
Yes, if the OP liked to have a bit more bass in his music, going with floor standing speakers would be the only change in my recommendation. It would likely add $200-300 to his speaker budget, but worth it if bass is important. He has already nixed a subwoofer as too complicated.
Eh, maybe not. These floor standing speakers are only $150 each. That’s the odd thing with speaker pricing, bookshelf speakers are usually priced per pair, floor speakers are priced each.
I wonder if it’s possible to buy anything like these mini floor-standing DIY speakers?
http://trevormarshall.com/ground-effect-omni/
They were featured on “Hack-a-Day”
Most all of my cassettes became available on CD. I tried to get one like yours transferred at a place that did that sort of thing back in the 90s, but was unsuccessful.