HI! What! No melee weapons, lets just throw flowers at our foes and hope they sneeze to death!
OK, OK, No melee weapons, then definitely the crossbow. The longbow is nice but takes a long time(year or two) to learn well. The crossbow and its bigger badder cousin the arbalest takes about a week to learn. The downside of both these weapons is the size and rate of fire, the arbalest more so, as it takes a block and tackle arrangement to draw, up to 1100 pounds pull compared to 150 to 250 pounds for lever drawn(i.e. goat leg) crossbow.
Another weapon to consider is the simple sling and staffsling. It takes a bit of practice to use a sling but I have found them to be very accurate after a little practice, the staffsling more than the sling as it doesn't need to be "spun" and released for its momentum. For longer range and/or more "firepower" the staffsling is the only way to go. It is one of my favorite "ancient" weapons.
The staffsling and sling are both concealable(the staff for my "bad leg" and the sling, "Why thats my headband, eyepatch, or homemade hernia belt."
) and deadly in the hands of a practiced individual, but then again so is a metal bodied writing implement and pointed stick, but I digress.
There is nothing like throwing a fist sized rock 75 meters accurately or at 10-15 meters against a concrete wall in a 8 inch group and making the rock split with a staffsling. I recommend you make one and try it out. I was very surprised as to their effectiveness, especially the staffsling.
Note: It is more that likely illegal to make and use a sling and staffsling in your local(the sling by name, the staffsling by default, at least in my area), but if nobody is looking I say go for it.
Most police nowadays do not look at the sling or staffsling as a weapon like they did in days of yore(How long ago is yore?.) In my fathers day(yore), late 40's early 50's, they used to stop him if they saw him with his sling. He took 2 rabbits and lots of chickens(had to kill them for dinner anyway, might as well make it sporting) with the sling he made when he was a kid.(I have it now) That is before he got to use my grandfathers .22(500,000 rounds and still shooting, I have it too)
For more info in the crossbow try this webpage:
http://snt.student.utwente.nl/campus/sagi/artikel/faq/crossbow.shtml#Books
or this book:
THE CROSSBOW
by Sir Ralph W. F. Payne-Gallwey, Holland Press, 1903, 1958
and also reprinted in the 70's.
As for the sling try:
DAVID VS. GOLIATH the Bible, various printers.
I know of no text expounding the staffsling, if you know any please enlighten me.