My first personal synthesizer
Technically the first synthesizer I had access to was a Ralph Dyck designed 3-oscillator modular synthesizer. This was through a "non-traditional" composition course that delved into Musique Concret and Electronic Music. This was in grade 11 and 12 of high school. That course taught me so much about deconstructing music compositions and how to think about sound in general. Many of my classmates were non-musicians which really opened my eyes. And, when lusting after a synthesizer of my own was no longer bearable I scraped together $400 to buy an A.R.P. Explorer. This was a single-oscillator synthesizer with an octave dividing circuit giving me 4 octaves of the same sound at once. 4 Waveforms could to be combined as well; "Brass" (Saw), "Hollow" (Square), "Reed" (Pulse) and "Fuzz" (PWM-ish). This was pretty effective and a good starting point.
To thicken things up I bought a Clone Theory chorus pedal which worked surprisingly well. As did running through the Leslie amp and speaker. I bought this when I was about 16 and along with my Hammond, could cover a very wide array of contemporary sounds when playing in rock bands. The Cars were hitting the airwaves and their accessible keyboard sounds were dynamic and reasonably easy to reproduce. I learned a lot. Within a few years I took the Explorer and modified it, heavily, into a portable synth or 'Keytar' as they would eventually come be known. I dubbed mine the "Walkabout" as an homage to the Australian movie I saw as a kid. Any inexpensive synthesizer can serve as a great place to start, to learn about sound design and to develop a personal keyboard style. I now had 4 actual keyboards I could configure to cover just about any kind of gig. With my driver's license my music education continued in leaps and bounds.