Most effective for what?
Regardless of whether your goal is to lose fat or gain muscle, scientific sports research has proven that squats and deadlifts offer you the best bang for your buck if you're really pressed for time. If you want to up the ante, try heavy sets of clean & press.
For squats, if you don't have a squat rack, you can do front-squats (clean it and then squat with the barbell), hack squats (grab the bar from behind your back and make sure the bar hits the back of your legs so your back won't hurt -- this looks like a deadlift with the bar behind your back), or dumbbell squats (hold two dumbbells then squat).
For deadlifts, a good version is the wide-grip deadlift. It sounds exactly what it is: you grab the bar near the plates. This will boost your strength significantly and add muscle to your body like nothing else.
Clean & press is done like this: grab the bar on the floor with a width that you're comfortable with (you'll look like you're about to do a deadlift), take a deep breath and pull with all your might (let momentum help you, trust me, it's part of doing a clean because you have to do it fast), once the bar reaches your thighs/waist your traps will automatically come into play and power shrug the bar (just let it travel up, up, up), bend your knees as much as possible and go under the bar, catch the weight in front of your chest, stand up.
That's the "clean" part. Now for the "press": With the bar resting on your chest/clavicle, take a deep breath and brace yourself, bend your knees a little, drive upward with your legs while pushing with your shoulders at the same time. The bar should now be held at arms' length over your head. Congrats! That's one rep of clean & press.
The above exercises are really hardcore and will turn your body into a fat-burning, muscle-building, strength machine so don't shy away from them! Google it if you don't believe me!
These exercises will work your entire body so much that I would even go far as to say that even if you don't do anything else, you'll be in the best shape of your life. You can structure your workouts like this (just a suggestion):
Day 1
Squat (any variation) 3 sets of 5-8 reps
Day 2
Deadlift (any variation) 3 sets of 5-8 reps
Day 3
Rest or push-ups (3 sets of as many reps as you can)
Day 4
Clean & press 3 sets of 3-5 reps
Day 5
Squat (any variation) 3 sets of 5-8 reps
Day 6 & Day 7
Rest or push-ups (3 sets of as many reps as you can)
