Great. This is a really cool analog lab project involving a wide range of interesting circuits, but there is a right way and a wrong way to spend your (valuable) time doing it.
Here's the deal: There are four characteristics that make sounds interesting from a musical point of view: pitch, volume, polyphony, and timbre. Everybody knows what pitch and volume are. Polyphony is the ability to play independent voice parts at the same time. Timbre is the quality given to a sound by its wave shape, envelope and overtones.
Since most of us were introduced to producing music through piano or guitar, we often consider polyphony to be more important than timbre. Besides, if we want to play harmony and chords (as we're used to), we will need a polyphonic synth. Often, this thinking leads to students building projects that consist of 40 identical oscillator circuits, one for each independent note. This is not a terribly challenging, interesting or efficient use of your time.
The quality that actually makes sound interesting to listen to is timbre. The difference between a played on a piano, a trumpet, a violin, a snare drum or a vacuum cleaner is the timbre. To get maximum flexibility out of your synthesizer, what you really want is not a synth that can play a lot of different notes at once, but a synth that can produce a wide range of timbres.
Thus, the preferred method for building an analog synth is to build a single voice, modular synthesizer that has maximum flexibility to adjust the timbre of the sound. This is how the ``classic'' analog synths (MiniMoog, ARP 2600, Roland SH series, etc.) were designed. A good audio oscillator is key, but you also want modules that can filter and shape the sound and process the signal in weird and interesting ways.
The most common modules in analog synthesizers are VCOs, VCFs, VCAs, and ADSRs.
VCOs are voltage controlled oscillators (the output frequency is voltage controlled, usually from the keyboard) and are the primary signal source for your synth. You will probably want more than one, because a couple of VCOs running at slightly offset frequencies (offset by a fifth, octave, or even a major or minor third) can create very rich textured sounds. The output waveform is sometimes sinusoidal, but is usually chosen to be a waveform rich in harmonics, like square, triangle, or sawtooth. Sawtooth oscillators are usually preferred because they produce both odd and even harmonics of the fundamental.
VCFs are voltage controlled filters and are used to filter the VCO output as low-pass, band-pass, band-cut or high-pass filters. The cutoff (or center) frequency and the filter resonance are controlled by the input voltage, which can dynamically change the harmonic content of the note as it is played.
VCAs are voltage controlled amplifiers and are used to create an evolution in volume as the sound is played. ADSRs are envelope generators (named for their function: attack, decay, sustain, and release) that are used to control the VCF and VCA modules.
Other modules that you may be interested in building are low frequency oscillators (LFOs), white noise generators, ring modulators, and glides (portamento). LFOs are used to modulate the control voltages to the other modules (VCO, VCF, and VCA) to provide tremolo or vibrato effects. White noise generators can be used as additional signal source, usually mixed with the output of the VCO to add the whoosh of a wind instrument or the the crash of a cymbal or drum. Ring modulators are basically analog multipliers that create very weird effects, but are important for synthesizing things like bell sounds. Glides are used on the inputs of VCOs to provide trombone-like slides from note to note.