If you only memorize one table I would suggest the one below. It can be played effectively under any rules. To use the basic strategy look up your hand along the left vertical edge and the dealer's up card along the top. In both cases an A stands for ace. From top to bottom are the hard totals, soft totals, and splittable hands.
Rule variations can have an effect on some borderline situations.
The most flexible rules are the number of decks, whether the dealer hits or stands on a soft 17, and whether doubling is allowed after splitting. Some obvious situations have been left out to keep the chart as small as possible. I have more basic strategy charts for other numbers of decks, as well as European blackjack. The best way, I have found, to memorize the basic strategy is notice patterns and to try to understand why you should play every situation as the chart says. Then make flash cards and go over and over them until you know it cold.