Having just started this myself (also with prior experience doing visual), I'll concur that it is a slippery slope greased with money. That said, I've tried to future proof my purchases, so I shouldn't outgrow things quickly.
Your budget could get you an AZ EQ6 GT from the right dealer with maybe a hundred or two left over. If you went for a NEQ6 instead, you could get a 8" reflector too.
Problem is you also need a camera, guide camera, light pollution filters, guidescope, coma corrector, laptop, dew heaters........
Well
need is a bit strong, but you'll need a camera at least.
Another route is going second hand - you could probably manage a decent basic setup if you picked up a second hand mount (NEQ6 is good) and OTA out of the classifieds here. Would leave plenty for a new DSLR and even a few of the other bits and pieces.