Heya,
Well, since you need a processor (receiver/AVR) it would be to your financial disadvantage to attempt to get active monitors. You will not build 11 channels surround with 4 subs on a budget receiver, that requires at least a $1.2~1.5k receiver/AVR and it would have to have pre-amp output to feed out to your monitors. Since you are already bound into this, to get 7.X.4, you will save a lot more money by getting passive speakers to let the AVR power; just get efficient ones and this will help with budget on speakers; again since you're wanting 11 channels (11 separate speakers: Front L& R, Center, Side & Rear Surrounds, Front and Rear Atmos Pairs). The only inexpensive way to do this would be to drop down to 5.1, no atmos, and get a $300 receiver/AVR and passive speakers. But if you're set on 7.X.4, you're looking at $1.2~1.5k minimum for an AVR/receiver that has the processor to do this. And no non-AVR processor exists for under $2.5k that will do 11 channel processing.
So basically I would drop the active speakers idea from this based on your plans, as you're just throwing money away doing that since you will already need/have a receiver with amplifiers for this purpose if you buy a processor for surround/atmos.
Very best,