One of the best reference sites out there is EveryMac.com They have a very reliable and comprehensive list of pretty much every Mac product ever made.
You should take some time to review and become familiar with the specs of your machine.
You aren't going to get a very modern OS X experience out of this machine.
- The latest OS X version that's compatible is 10.7 (Lion)
- Max RAM is 3.5GB
- HDD is SATA I (1.5 Gb/sec)
No matter how you slice it, it's not a strong platform to begin with.
All is not lost. It's still a good laptop to be used for surfing the web, checking email and even doing some office type work.
- 4GB of memory is cheap (2x2GB PC2-5300])
- A New battery is around $50 on (don't ever buy used batteries, it's not worth it)
- A SATA SSD can be had for as little as $45-50 on and even cheaper on eBay used.
With these few upgrades, you can install Windows 7 32bit (potentially Win10, but I haven't tried it), Ubuntu, or my personal favorite FreeBSD (you will probably have better results with *BSD since OS X is based on the BSD OS). In fact, if you are looking for a machine in which you can learn one of the *NIXes, this is a great way to do it.
If you are looking to keep it in the Apple family, just be aware of the limitations on it. You will be using an OS that is now 7-8 years old and 3rd party apps which are long since deprecated and no longer supported.
If you want a modern experience, you can do some minor upgrades and install Windows, FreeBSD, or Linux on it and keep going with modern software.