I started with the 3x3x3 video by Noah Richardson (linked below) and was able to solve the cube in 2-3 hours after I had written the instructions down on paper and only using the paper as a cheatsheet. Memorizing the cheatsheet and being able to solve it completely by myself took another day of on and off practice. I would memorize and practice one sequence/algorithm at a time, until I memorized them all.
The 2x2x2 has fewer steps and is easier to solve. I think it's a good beginner's cube. Some of algorithms are also very similar to the 3x3x3.
Don't buy the Rubix brand - buy a speedcube instead - they are much more forgiving and takes less effort to turn, and will help a lot when you are practicing. These are what I bought after doing a little bit of research online:
- 2x2x2 - https://www.amazon.com/gp/product/B06XP21H54/ref=oh_aui_detailpage_o00_s01?ie=UTF8&psc=1
- 3x3x3 - https://www.amazon.com/gp/product/B01DJFVSQC/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1
- For the 2x2x2 - I found this article - https://www.youcandothecube.com/solve-it/2-x-2-solution - even better than the video posted below duo to the illustrations. Note: the last algorithm is different from the instructional video.