I love eating paleo and am now ready to experiment by adding the best exercise to this lifestyle. Where's the best place to start....yes I am currently out of condition :)
I highly recommend starting with Mark Sisson's Primal Blueprint Workout Plan. It's really simple:
For sprinting: I recommend finding a grassy field and running about 25 to 50 yards as fast as you can. Then walk back. Repeat! Start with three and work your way up to ten.
For lifting heavy things: you might try joining a cross-fit gym (I hear they're good with newbies) or get a good set of hand-weights. Also you could look into body-weight exercises. I try to lift really hard (within reason but without taking a break) for ten to fifteen minutes. I do squats, push ups, pull ups, and other simple things.
For moving slowly: you could go for a walk, a hike or a jog. Whatever you feel like! Or just rest on this day! Recovery is an oft underrated part of physical improvement.
The schedule above suggests doing each type of activity twice a week; but if you'd like start slower, you could try doing each activity once per week! Best of luck!
I recommend "Body by Science" by McGuff.
His approach is based on very intense workouts, but only once a week or so. He says that working out too often is a common problem, and that it does more harm than good, because it doesn't allow the body enough time to fully recover.
You can find a good intro to his approach on YouTube.
In my opinion, stronglifts.com. In order:
Lifting weights has helped my posture, back aches, strength, weight and endurance. Crossfit is also great, but I prefer stronglifts, as I hate to exercise in a group at a set time. Also I fear burnout, which I've heard some people get with Crossfit. Starting a weight lifting program would also be good preparation for Crossfit.