>My other question is whether I might be better off
> trying to run a cable between the two buildings..

Cable is always the most certain connection if you are willing to do
the work. You can still hang an Access Point off of it at the shop if
you want. wireless there.

Powerline networking is 3rd option to consider, more reliable than
wireless if your wiring supports it.

>I have plenty of
> two wire electrical cable (which I presume is not the right stuff) and
> also have 6 wire telephone cable.

There are others (Jeff ) on this forum that can tell you how to do
this with above cables. I doubt it's worth it unless the other cables
are already installed to the garage.


> Does anyone have any thoughts as to how I can best approach this
> situation..

Assuming line of sight, do a test -
1) Put a reflector on your existing router and put it in line of sight
to shop- a window facing it, for example.
2) Take a laptop, connect it wireless to same router and walk over to
the shop. Watch the signal and note when the connection drops.

If it makes it all the way to the shop where you can use the
connection, then the solution is simply a router/reflector in your
home's window. If it does not make it, then I'd go with cable or
consider powerline networking.