Same background here as yourself and Blackburn37, and seconding his points. If you're needing to save money, I wouldn't worry about going pure analog (unless you want a cheap mono like a Microbrute).
You might want to pick up an 88-key controller with a nice touch and use it to control something like Omnisphere, which would probably be my #1 recommendation.
You're not going to come close to the touch of a nice grand with anything (as good as the touch is on something like my Yamaha Motif XS8), and it's unlikely that you'll be playing anything particularly virtuosic on a synth so those shouldn't be your goals. I'd definitely recommend getting the educational discount on Syntorial and working your way through that. It's a fantastic way of really developing an innate understanding of subtractive synthesis and is more immersive than watching any YouTube video and has advantages over reading books because it consistently tests you along the way.
In general, as far as inspiration and value for money goes, it's hard to beat Omnisphere and Native Instruments Komplete (11 or 12) and a MIDI controller, but I'd probably suggest picking up a nice affordable digital workstation like a Yamaha Modx (nice touch too) or Korg Kross/Krome, which can be used effectively both live and as a studio MIDI controller.