Free: Contests & Raffles.
Depending on the age of your bow you may want to avoid any of the low/no stretch strings. B50 or B55 dacron is a safe bet for an older bow. The B55 has a little less stretch. With a 40# bow you should be able to use a 12 strand string. A 14 strand will work, but the extra weight will slow things down a little. 52" is short for a recurve. You may want to consider using three fingers under the arrow, and dropping the bottom finger before release to ease finger pinch. I could put together a string for you, heck if I look I may have one, but I don't know how I would get it to you.
3Rivers sells the endless loop strings for pretty cheap . It's a good option to see if the bow will work for you , I find that the serving on the end wear out pretty quick with lots of shooting but if you like the bow you can move up to a better string later .