There should have been an AMO bow length and poundage on the riser. Might have worn off or been refinished. I assume the 52.5" measurement is an end to end (straight line) measurement?
The "black plastic" is most likely phenolic or linen micarta--both heavy, durable materials still used in some bow risers today.
The proper way to measure a recurve is start at the "top" of one string groove (with a flexible tape measure, like a steamstress' tape), follow the curve of the limb, through the middle of the riser, follow the curve of the other limb, to the "top" of the other string grove. That will give you the AMO bow length. Proper string length will be between 3" and 4" shorter than that measurement.
The poundage might still be labeled behind the strike plate, unless it was removed. If so, the only way to find out is measure it on a scale. Any bow shop should take care of that for you for free.
Unfortunately Pearson hasn't offered traditional bows in many years. No idea what the one you have is worth--I'd guess between $100 and $200, but it's just a guess. For some reason Pearson bows didn't hold a collector's value like some others.
I really like old Pearson bows, but the short bows can be finicky, especialy for someone starting out. Depending on your draw length, I'd go with a bow no less than 60", 62-64" might be better (depending on the bow design). The Samick Sage is a good bow, very reasonably priced, and since it's a take-down you can change out limbs later if you want.
Sounds like a nice old bow--good luck!
Chad