Room Correction

I have been having a tough time choosing speakers, a lot to do with a somewhat difficult room. Good size, but tight speaker placement within an area not allowing for a lot of space off back and side walls. Plus a lot of windows and hard surfaces (flooring, etc.)

I listen on a much more casual listening and not one specific sitting area within the room.

I listen to a lot of vinyl and streaming.

The idea of running analog through a digital room correction seems very strange to me, and does not sound appealing. Although I can be easily convinced otherwise if this is just a misconceived idea in my head. 

The speakers are in my main living room so a lot of significant treatments are really out of the question. 

What would you do to get the most out of your speakers in this setting?

What are some of the best room correction devices? treatments? items?

If budget gets limited after system purchase, what items will give me the most bang for my buck in the room?

Thanks so much!