Honestly the Genelecs are past the desired budget, before factoring in subs, which I hoped were not necessary. So if I’m not going to get fantastic results out of this, it’s probably not worth me spending the money on it.
If the big Genelec are too expensive, I can think of a few good value alternatives.
Room correction with Dirac is easy to setup and, in my experience, quite efficient.
MiniDSP has some hardware with Dirac included, be it integrated with a DAC or standalone (to insert between the source and the DAC, as an example).
Speakers wise, a pair of Genelec 1032 may be found used for quite a low price.
I was able to buy 2 pairs of 1032A for around 1500€ each in the past.
They are good active speakers that, as long as you don't install them on the floor, will give you a good and loud sound. Especially with Dirac.
If you prefer, passive towers may be a good choice too.
If you're in Europe, I'm quite happy with the Focal Aria 948 (with Dirac). But there are plenty of other options.
Add a good amp (Purifi ?) and you'd be very good...