Craig, welcome. Yes, your Axioms will certainly provide the way to enjoyment of great music. The f15 sub should provide a similar step-up in quality and bass extension.

The 2112 and 2312 would both be fine receiver choices and you might also consider the Onkyo 709, which would probably be one notch up from the 2312(including pre-outs if you'd want to use the old amps you have).

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Enjoy the music, not the equipment.