Re: What is the correct way to put a buffer before the circuit?
It depends what you're trying to achieve.
If you just want the Rat to have an input buffer (to avoid squealing, for example), then you can put the buffer between the switch and the main circuit: input jack -> switch -> buffer -> Rat board -> switch -> output jack. (Alternatively, you could just build the buffer into the main Rat board. But that would require a modified layout, and it looks like you've built the Rat circuit already and have a separate daughterboard for the buffer.)
If you want buffered bypass, you can put the buffer between the input jack and the switch: input jack -> buffer -> switch -> Rat board -> switch -> output jack.
These are my two top guesses about what you want, but there are other possibilities. If neither of these is what you're looking for, let us know what you're hoping to accomplish with the buffer and we can better advise you.