I am launching a For Sale By Owner real estate website.  As part of
the fee that I will charge sellers who list, I will send a "For Sale"
yard sign and two directional signs with my company logo on them.

What companies can manufacture these signs at an attractive price?
Can the manufacturing company also mail the signs to my customers if I
give the company a list of addresses on a daily basis?
Or, should I have the manufacturing company mail the signs to me and I
can then mail them out?
What is the most efficient form of mailing?

Scoutsdad,
"Yard signs for realestate sales" may suggest different things to
different people, from more or less weatherproof cardboard (to be
later disposed of), to plastic (like those ready-made "For Sale" signs
one can buy at hardware stores, of course, larger and "fancier" in
your case), to the kind of signs other realtors use, and probably
reuse, such as these from a Sponsored Link to your question:
http://coldwellbankersigns.com/
But I expect that these are not what you want, i.e, that you will
leave it up to the owner/seller to place the signs.
By "directional signs" I imagine something simpler to be posted at the
next street corners, which I expect would be disposable/dispensable,
since it can be expected that they will not survive for reuse.

Perhaps you can explain what kind of signs you are envisaging.

Whoever makes them, I expect that they don't want to get involved in
individual distribution.  They will offer prices for 25, 50, 100,...
signs and assume that they can deliver them all to you.  Naturally,
the price/sign will be less the larger your order is.
If the signs can be bent to some extent (into a U or circle pressed
down in a carton), it  might be interesting to talk with UPS and Fed
Express about the size and prices for their standard cartons to
discover the optimal size for the signs relative to shipping price. 
(No reason choosing a size that is an inch or two too big to fit in
the next smaller carton.)
 Good luck,
  Myoarin