Rather than rolling your own password system, I would recommend diceware.com for strong passwords (including master passwords) that you can memorize (I am bad at memorization, and have memorized 129 bit passwords this way, and 64 bit passwords are kind of a breeze to memorize).

For the long tail of passwords that you shouldn't be memorizing in the first place, a password manager with a good configurable password generator is invaluable. I use Lastpass (I like the breadth of it's platform support: all major consumer OSes, all major mobile OSes, extensions for all major browsers). Alternatively, lot of people recommend 1password.

Diceware has better guarantees, but the password managers are usually much more convenient[1]. I weigh these costs and benefits when choosing which way to go for a particular use case.

[1] With the significant exception of passwords that will regularly have to be typed out on mobile, since diceware passwords are much more virtual keyboard friendly than random character generated passwords. This is partly because you can typically keep the entire thing in your head, not having to reference your password manager multiple times, and partly because they don't rely on special characters for their entropy, so can be typed out on the primary keyboard without switching to numeral or special character keyboards.