I think you might need to provide some more context and information on your goals in order to drive more discussion and suggestions. Perhaps including mention of some things you've read and considered.
Recommendations for a replacement AVR will depend on factors like the specific speakers you're using, their sensitivity, impedance, your room size, listening levels, etc. People do try to make recommendations at many price points, but often the cheapest mentioned are in the $500 range. People tend to suggest the Denon AVR-X3500H, for example. You could do searches on that, the 2500, the similar Marantz models (5013/5014), and Yamaha 1080 maybe. There are other options sometimes mentioned if you are willing to just 5.1 instead of 7.1 etc.
I haven't seen many projector recommendations here. Perhaps in some of the other sections. Sites like ProjectorCentral focus on projectors, do reviews and have recommendation lists in the sub $1,500 and sub $750 categories.