Quickest Way to Gain Strength
The best way to gain strength, assuming you are not an experienced lifter, is with Free Weight workouts. I would do 2 or 3 full body workouts a week for four to eight weeks concentrating on compound movements like Squats, Deadlifts, Bench Press, Lat Pulldowns and Rows. Complete 3 sets of 8 reps per exercise and don't worry about isolating arms and legs at this point, that comes later.
Drink a Whey Protein shake within and hour of your last lift and first thing in the morning when you wake up. There is a book titled "The New Rules of Lifting" that is practical and informative.
Good luck and happy lifting