A word of advice: Purchase a newer used or refurbished Mac computer fully capable of running OS X 10.8 Mountain Lion, and preferably with 10.8 already installed, so you can see how the system performs.
The oldest compatible models for OS X 10.8 Mountain Lion are listed by Apple here:
System requirements for OS X Mountain Lion
You can always choose to install the free OS X 10.10 Yosemite upgrade later.
https://www.apple.com/osx/how-to-upgrade/
Instead of buying random parts that might not even work together, save your money until you have enough to purchase a complete newer Mac system that was designed for the newer operating system. While the absolute minimum RAM specification for Mountain Lion, Mavericks, and Yosemite is 2GB, they will run MUCH better with at least 4GB RAM.
Trying to convert a 7- or 8-year-old computer to run a current operating system is a huge waste of money, time, and effort. Parts for old MacBooks are expensive. There are many minor changes between models that appear to be the same on the outside, making it nearly impossible to put just one part from a newer computer into your older case. The "unibody" white MacBooks from 2009 and newer that WILL run Mavericks and Yosemite are VASTLY different inside than your MacBook 1,1. There are multiple reasons why Apple chose not to extend backward compatibility to Mac models as old as yours: Limited processing power, limited graphics capability, and limited maximum system RAM.