Unfortunately a 2008 MacBook is only able to install up to OSX 10.7.5 which was a paid upgrade. You are much better off running OSX 10.6 especially if the laptop will be used to access the Internet since 10.7.5 has an unpatched vulnerability. AFAIK, the only web browser that may still work to get online is TenFourFox and I think it will need OSX 10.6. You will need the retail version of the OSX 10.6 Snow Leopard DVD if you want to install OSX.
Another option if you want a current OS and to be able to use the common web browsers such as Google Chrome, Firefox, and Vivaldi is to install Linux on the laptop. However, this will require you to learn a new OS. Linux Mint or one of the Ubuntu flavors such as Kubuntu or Ubuntu Mate are good choices to use on a Mac with limited memory. These Linux distributions allow you to test them out from the installer USB stick so you can see what it looks like. Keep in mind running Linux from a USB stick will be extremely slow so know that Linux will run faster once installed to the internal hard drive or SSD.
Keep in mind 1GB of RAM is not ideal even for Linux especially since 144MB of memory is used for video memory. I did use Linux on a 2009 MacBook with just 2GB of RAM and it worked surprising well to access the Internet. 4GB is definitely the sweet spot though.
I really would not put any money into this laptop. However, if you are going to upgrade the hardware, then I recommend using the OWC Mercury Electra 3G SSD since it will be the most compatible SSD since this SSD uses a SATA II controller which is also used on this Mac. The only other SSD I would even consider would be a Crucial MX500 series, but there is a chance it may not be compatible with such an old system. Stay away from the Crucial BX500 series as it is an awful drive.
Also only use memory from either Crucial or OWC since Macs are very picky about the memory they use.
Edit: I forgot to mention that you can clone the original hard drive using Carbon Copy Cloner. You will need to download an older version of the app which is compatible with OSX 10.6. The older version is available on their website here:
https://bombich.com/download#unsupported