Burpees:
http://www.bodybuilding.com/fun/rossboxing2.htm
Natural glute/ham raises:
http://www.bodybuilding.com/fun/renegade10.htm (scroll down a bit and you will see it)
Reverse hypers (from a T-mag article by Catanzaro):
"If you want to increase your strength, speed, power, reaction time and add some muscle mass, this is the exercise. The reverse hyper was popularized by Louie Simmons, who has produced some of the strongest powerlifters in the world at his Westside Barbell Club. This exercise thoroughly stresses the posterior chain of muscles (erectors, glutes and hams).
Some strength authorities believe the reverse hyper has greater specificity to sport with respect to hip extension than other popular exercises such as the Romanian deadlift. For instance, strength coach Kim Goss feels the reverse hyper is an excellent assistance exercise that doesn’t compromise technique on the Olympic lifts. It’s an effective exercise that can be used by many athletes to improve their performance.
You can perform the reverse hyper on a dedicated reverse hyper machine (refer to Dave Tate's site for more info) or simply perform them on a regular back extension machine by positioning yourself backward. I've even had clients do it over a high counter or bench. Just make sure that you have something sturdy to hold on to. It can even be performed over a large Swiss ball, but use a Swiss ball only if you don’t have access to a reverse hyper or back extension machine (or even a high bench for that matter!)
Unfortunately, the ball tends to absorb and dissipate some of the force from the working muscles as well as shift too much stress onto the shoulder stabilizers. This detracts emphasis from the hip extensors. Furthermore, in order to carry out the vital ballistic recoil action during this exercise, the legs should be able to swing right underneath the body to effectively prestretch the hip extensors. Thus, the Swiss ball is useful only for fairly slow, limited range hip extension movements.
A Swiss ball is great for rehabilitation, however. Typically, the tempo can be slow and controlled, favoring isometrics if the aim is rehab. Perform two to three sets of 10 to 12 reps with a static hold of 5 to 10 seconds at the top. Keep the rest intervals fairly short (up to a minute) and don’t increase the load (i.e. by using ankle weights, or a dumbbell or medicine ball between the feet) until you’re able to complete 12 reps with 10 second isometrics (which equals 120 seconds or 2 minutes time-under-tension.)
This exercise is considered quite safe since it encourages a natural concave (as viewed posteriorly) lumbar curve at the point of greatest overload. By reducing the lever arm and bending the legs, greater emphasis is placed on the glutes. Allow this only if the individual is unable to keep his legs straight. A progression would then be to straighten out the legs over time. In fact, many physical therapists use a simple test of palpating the hams and glutes while performing hip extensions (essentially the reverse hyper.) If the hamstrings contract first and the knee subsequently bends, there’s generally weakness in the glutes."
In regards to frequency and the 3 non-consecutive days per week, I favor varying the intensity.One approach is the heavy-light-medium day system.The specific day can dictate the level of intensity or the amount of volume you should perform.The heavy day can either be a personal best day, where you go for a max weight or max number or reps, or more appropriate for bodyweight exercises, a highest volume of the week day.You shoot for a specific amount of reps per exercise and the following heavy day, you attempt to better this amount.
Your light day is a sort of recovery day where you are basically just keeping active with a small amount of exercise and maybe focus on your form or technique.
The medium day is of higher intenisty than your light day but not greater than your heavy day and acts as a "set-up day" for the upcoming heavy day.
I favor full-body routines for the most part but you could also do splits.I wouldn't go past the point of divinding your workouts into upper body one day and lower body the next.Further specialization is getting more into the area of bodybuilding in my opinion.Stck with full body or an upper/lower split and you should accomplish plenty.
Also, I would encourage you to inject lots of variety into your workouts.Doing the same thing over and over will make you go stale and lose interest.Get some variety going.Don't just do pull-ups for instance.Alter your grip to include palms in and palms facing each other.Throw a towel over the bar and grip each end in your hand as you do your pull-ups.Load up a backpack with a small sandbag or a couple of bricks and wear it while you do your pull-ups.You can also play with the sets and reps by implementing ladders and pyramids as well as doing circuit training or super sets.Keep things intersting and your motivation will stay strong.