The wood bow is iffy--it might hold up, might not. If it has sentimental value, I'd put it away. Lancaster Archery, 3 Rivers Archery, Kustom King Archery, etc. all offer kid's bows at a reasonable price--probably cost much less than the Pearson is worth to you.
I couldn't say what model it is, but obviously it's an older one since it's solid wood. Probably not worth a lot as far as collector's value, but still a nice piece.
60" bow is supposed to get a 56" string, but that can vary. The old "rule of thumb" is 3" shorter for longbows, 4" shorter for recurves, but AMO says 3" shorter for either one. Problem is, lots of stores and string makers don't know how (or don't care) to measure a string by AMO specs, so it can get confusing. Generally speaking, for an old Pearson longbow you want a string 3" shorter, for an old Pearson recurve probably 4" shorter. Dacron only--either B-50, B-500, or B-55.
If you need more help with strings, just holler.
Chad