Don't think of it as "I already have the keyboard", because you'll be reducing your options. The big majority of synths come with keyboard, and few have a keyboardless model. I'll include keyboardless models here, but don't get too fixated, you might find another option to be better.
First note that you don't need a MIDI to CV module to control hardware synths, since most are MIDI compatible. Only specific modular systems need MIDI to CV conversion, but if you don't have the money for a MIDI to CV module chances are that you don't have the money for the full modular system.
The Portable-11 from synthesizers.com, for example, is at 1,700 USD, and I think it's the cheapest good quality modular you can get (it includes the MIDI to CV convertor). The MIDI to CV alone is around 260 USD.
But you don't have to go modular. There are many non-modular analog synthesizers out there that are MIDI compatible. We can look at some quality budget models like:
Polyphony is not common in analog synths, and when found it is very limited and probably expensive. The timbre wolf above has 4 voice polyphony, the other are monophonic.
If you want more polyphony, and other extras, you want to check virtual analog synths, which are digital and emulate the analog quality. The cheapest quality options are:
Virtual analog synths often include extras like effects, sequencers, vocoder, more oscillators, more modulators and modulation capabilities, more polyphony and voices, etc. They might not be able to perfectly emulate some analog dynamics though (filters can sound very different). So, if you are going for a very specific analog sound, make sure that specific model of virtual analog synth can produce it before buying it.
In general, it's a good idea to test and listen to the synth and make sure you love its sound before buying it.
And regarding schematics, if you want to go the DIY route, you should take a look at this book:
It is very accessible and easy to follow, teaches you to build a basic subtractive synth: LFO, VCA, VCF, VCO, LFO, etc. It should be the less expensive option, if you can get a good price for the components, but it's also the less flexible model. The experience of building one is more than worth it if you are into this kind of stuff.
You might also want to consider going software synth. There are many excellent software synths and synthesis environments, including virtual analog software synths, many of which are free. Can't get cheaper than that!
You already have a MIDI keyboard, you already have a computer, so you are already good to go. You can buy a MIDI control surface to control the synth, if mouse and keyboard is not your thing.
There are countless software synths out there, this should be a good starting point:
