This is easier and MUCH more terrible, but much easier and cheaper.

A First Act GoAmp (it'll turn on when you plug a guitar in)...

(You said cheapest and easiest, so...)

as for the switch and headphone jack you can add those very easily... for an on off switch all you need to do is wire a switch with the positive from the battery that cuts it in one position and lets it connect to the circuit in the other.
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