i didnt want to give a single sentence half thought through response, so i did a bit of a deep dive into 'generative'. it seems to me like it can mean anything from random, quasi-random, to procedural, and you have a lot of leeway in defining what it means for you. one option to consider is the moog labyrinth, it is a fully self-contained instrument, falls inside your budget, and gives you everything you need to start playing around with some of the many possibilities of 'generative'. (moog is a quite well respected brand, etc.) another option would be to really think long and hard about what you actually mean by 'generative', design your own custom sequencer in pd (pure data) controlled from a laptop, that you could then use some kind of interface to send cv note data out to a eurorack case, where you use your budget to create your take on a dark ambient voice chain signal path, something i dont know a ton about. i would recommend the strange-r bighat as a starting point for the generative aspect, but it already eats up into too much of your budget, all by itself. maybe check out the channel "not_a_creative" on youtube for some inspiration. unfortunately, i was not able to just design the perfect thing for you.
sorry. peace.
(edit)
{im not the right guy to ask about staying inside a budget. i tend to design stuff that ends up looking like this, etc.: ... ... ... ... ... }
