Newer versions of OSX are not going to always run well on unsupported Macs. Don't get me wrong they work but these older machines simply lack the graphic cards to always do well. Nothing run with trying the hacks though. https://www.youtube.com/watch?v=uESlYP1u... Personally I'd go with Linux. Elementary OS runs fine on these machines. This is cool: https://www.youtube.com/watch?v=-sR-uMTc9R4 Unless you have Apple software you have to run I'd move on.
While I love MacOS these older machines just aren't really designed to work well with the most current versions of OS X or MacOS. Yes you can get Mountain Lion , Mavericks or Yosemite to work but I suggest Linux or the nice, CloudReady. https://www.neverware.com/freedownload/ Here is a link to its use: https://www.youtube.com/watch?v=-sR-uMTc9R4 Windows 10 32 bt also runs well. A cheap SSD can be added for under $30.00. So unless you simply have to use OS X or MacOS. Try Linux or Windows or the great Cloudready. Linux and Cloudready are both free.
I sell Macbook duo cores on Craigslist. Most I load Snow Leopard on with a SSD but I dual boot Windows 10 and or a version of Linux. These machines tend to only have 2gb ram and run better with Windows or Linux then OS X. Snow Leopard, Lion and Mountain Lion are no longer supported by Apple. While the hacks can get you to Mavericks or beyond unless its a Macbook Pro I just wouldn't. Google reFind. Use it and Linux distros like MINT or Ubuntu or Arch and try them out. Take note of CPU and Ram use. Its lower then OS X. If you don't want to go through the hassle of making your Linux install look like OS X use distros like Elementary OS or Zorin or Pear OS. Windows requires extra drivers. Check out the Bootcamp updates or find drivers for sound, etc. on-line. On a budget? These units are around $50.00 on Ebay. A 128 SSD is $40.00 or less. Some have 4gb ram.
There are hacks such as Macpostfactor and others that can be used to place Mountain Lion, Mavericks, Yosmite and even El Captain on unsupported Macbooks, iMacs and even older machines. Look on Youtube for instructions. Many users have have great success with these methods.