[pmoriarty]

I'd consider getting a Eurorack modular synth.

Advantages:

1 - it's much more fun to build your own synth out of components than to buy an off-the-shelf system designed and built by someone else

2 - and you get to build exactly what you want

3 - there are literally thousands of modules to choose from, giving you much more flexibility and features than any integrated synth

4 - lots of cables to make a patch, which can be fun to mess with and interesting/intriguing for audiences to look at

5 - audio and control voltages are the same, so you can do things like change synth parameters with audio

Disadvantages:

1 - price, typically much more expensive to get equivalent functionality to a cheap integrated synth. [A]

2 - size - much bigger than a typical integrated synth [B]

3 - lots of cables to make a patch, which can make recreating a patch a pain compared to a digital/hybrid synth

4 - can look intimidating to someone unfamiliar with modular synths [C]

5 - making a modular patch can be slower than just dialing in a digital patch

Notes:

[A] - But you don't necessarily need to replicate everything, you can have partial functionality that will still be useful and fun, and may get effects that would be hard to get any other way

[B] - though Eurorack is still much smaller than some other modular formats

[C] - But it's not hard to pick up, and learning modular synthesis is fun

[joemi]

I'd add another advantage: The physicality of it all. That was what drew me to it. It's kind of related to your advantage #4 and advantage #2, but it's more than that.

The physical nature makes it easier (for me at least) to remember instinctively what does what. I've build my synth exactly how I want it... I've put module X right where I want it between module Y and module Z. Using it as often as I do, my muscle memory kicks in and my arms remember where things are. I can recognize most of the modules and controls by touch. It makes composing, experimenting and performing to be almost exactly the same process (at least the way I do it) - which is something I've been striving for for my entire musical life.

That said, I wouldn't actually recommend Eurorack to most people, simply because of the extreme price.

[pmoriarty]

The price issue can be mitigated in a number of ways:

1 - Buy used. You can get a lot of great modules in great condition used.

2 - Build your own, either from kits or (if you have the skills) from scratch. There are tons of kits out there, and you can make some pretty unusual and interesting modules with them. Plus, making your own helps you to understand them better, and help you to repair them yourself if they break.

3 - Limit your appetite for modules. You don't necessarily need a 4 voice modular synth, with 4 copies of every module. Try limiting yourself to one voice, or even to just a few modules that perform a small number of functions. That can still be really useful.

4 - (Related to 3): Combine your modular synth with an integrated hardware synth or even soft-synths. That way you can get the best of both worlds, and the non-modular synths can make up for what you're missing in your modular, again letting you limit your modular to just those functions that you need, thereby reducing the price of your modular.

5 - Buy from the less expensive module manufacturers like Doepfer. Their modules are often a fraction of the price of many other manufacturers.