The memory chip specs appear to be correct, though to be certain you'd need to purchase the RAM
from a vendor who guarantees and has tested the RAM (they sell) in the same computer build model.
If your Late 2008 MacBook (aluminum) 13-inch computer is the proper identification, that would be
Model Identifier MacBook5,1
Model Number A1278
EMC 2254
Order Number MB466LL/A (2.0 GHz), MB467LL/A (2.4 GHz)
Maximum Memory 8.0 GB (Actual) 4.0 GB (Apple)
Memory Slots 2 - 204-pin PC3-8500 (1066 MHz) DDR3 SO-DIMM
• MacBook: How to remove or install memory - Apple Support
Hard Drive Interface 3.0 Gbps Serial ATA (SATA)
For examples of correct spec memory chip upgrade see this OWC macsales product page:
http://eshop.macsales.com/shop/memory/Apple_MacBook_MacBook_Pro/Upgrade/DDR3
Notebook drive options - examples - appear here:
http://eshop.macsales.com/shop/hard-drives/2.5-Notebook/
If the computer had its EFI firmware update applied, the unit would support later OS X.
This may have already been applied in the past, you can see the version it would be if
installed, from the information in this article: MacBook EFI Firmware Update 1.4
The capacity of a replacement hard disk drive and rotational speed, at the interface level
may affect overall performance if too large and perhaps too slow. Though it should be
able to support the 1-TB HDD at 5400-RPM it may be a bit slow since that is where the
virtual memory or temp swap files would be written to and then read by the system. A
faster 7200-RPM or an SSD such as OWC Mercury Pro SSD from macsales, may result
in much better performance; though availability of storage capacities may vary in cost.
Sorry to not be of much help, however if you contact a good vendor as in examples above
they can help with specific information prior to any commitment to purchase, they're OK.
{hopefully you can upgrade your old MacBook and keep it running happily for awhile longer}
Good luck & happy computing! 🙂