Is there a magic formula for spending on components in a system

Try this to assess the sound in lieu of measurement gear:

https://ohmspeaker.com/news/thinking-outside-the-box-listening-outside-the-room-or-the-bouncing-sound/

It is true that, all else aside, it will cost more to get extended quality bass and quite a bit more for that in a large room compared to small.

That is because the amp and speakers both must work much harder to deliver extended bass and even more so for bigger rooms. 

There is no magic formula but if you want someone else with expertise to determine it for you consider an integrated device that you can just add most any speakers to.

A good example is the Bel Canto c5i which has high end sound and everything most any one might need already built in for a very reasonable cost, especially used.

Many other good ones also.  Just find one with the power and features you need.