Well what you asked are all very good ways to approach it.
I approach it with the divide and conquer method. I take a highlighter and try to indentify the melody, which hand is it in, and what voice. I usually highlight the melody with orange highlighter. Since the fugues can be a little tricky with tied over notes, those ties get the blue highlighter.
After this, I try to learn the melody in both hands, and then go after the rest of the voices.
I then play both hands together after a few times of playing hands separtely.
I would be very careful, in learning the correct notes. Bach is a little tricky in this. As for memorizing for me, I do not even realize the piece is memorized, until I begin to get bored looking at the music and my mind wandering off. I usually have most if not all learned, and only need a few spots of securing. Unfortunately, this is not a trait that is possessed by many people.
I would definietly master reading the piece looking at the music. When you get comfortable start to memorize it. Do not take a measaure at a time, take phrases. This will help you musically, and will take the "note, note, note" thing out and put in phrases.
I hope this helps. I am working on the C-minor prelude and fugue from book two. I liked the b-flat major prelude and fugue and c-minor prelude and fugue from book one. Eventually I would like to learn them all, and record them. Hope I can find the time.
Well see you later and have a nice day.
Topic: So I want to play a fugue