wrote

I plan on using Murphy's Oil Soap for the cabinets, TSP for the walls
(to help remove any leftover wallpaper paste) and maybe steel wool for
the edge of the counter?

Good luck in your new home! Correct on all but before you try the steel
wool (which may scratch), I suggest you first try:

1- Sponge pad with scrubber on one side (softer, wont scratch, may need
several sponges as they wear out and not sure how much counter edge you have
to do), possibly with 409. Coat with 409 and let sit for a bit. This may
be all you need. If you have senitive skin, you may want to wear some of
thse light weight latex gloves as you'll be in cleaner for quite a bit.

2- Check the label (or another will know and correct us here) but I think
it's bon-ami that is supposed to be scratch resistant cleanser? If the
above doesnt work, try that next with the scrubber sponge. Wipe all the 409
up first as one may have bleach and the other a bit of amonia.