There are several very good online articles that look at the historical origins of the "West Coast" vs "East Coast" comparison of synthesis. Dating back to the late 1960's this appears to have been largely used as marketing language to differentiate between the emerging design and compositional philosophies of Robert Moog (East) and Donald Buchla (West).
My top level takeaway from reading the below referenced articles (I will add to these as I find them), is that Donald Buchla was interested in the connection between the creative input (direct or remote) into sound generation (music, or whatever) by the means of highly flexible signal path with limitations which were imposed based on the technologies of the time. I view "Buchla Characteristics" as experimental in nature, often non-traditional, and occasionally very, very complex. At its heart is the influence of pseudo-randomness and uncertainty which leads to surprise discoveries through performative interactions. None of it comes for free though and I can see that this is life-long journey of restless, contemplative self-discovery.
There are plenty of hardware solutions to explore these avenues, but these are prohibitively expensive. My preferred means of exploration are through software solutions (which seem to fit very nicely into my view of what Don Buchla would consider appropriate today, but some kind of performative control is wanted) like VCV Rack (free standalone, or paid VST module). Reason has several modules (Complex-1 and Thor) which are capable of very interesting routing and patching options. I am also very partial to the sounds and routing that the Access Virus b (hardware) and Viper VST has to offer. And all of the above (VCV Rack running in Reason and through the use of Combinators can have their human interactions distilled down into a few specific controls to allow performative expressions of creativity. I am also pretty certain that Bitwig's internal Grid system can provide most, if not all, of the flexibility of VCV Rack in one self-contained environment.
My personal suggestion is to keep it simple (remove as many creative obstacles as possible - too many voices and needless complexity) and within your budget. It is assumed that you have access to a computer with Internet access, and a means of sound reproduction. I made decisions (choice of sound card and digital interface) more than 2 decades ago that have pushed me towards a Windows ecosystem, but if I were starting from scratch today I would get a decent Linux workstation would lean towards VCV Rack and Bitwig for a flexible creative platform.
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