Starting Strength is the number one best selling weight training book on Amazon. This is not surprising to anyone who is a student of weight training: Rippetoe has achieved a status of authority in his domain that is rare. The reason is that his program is low on bullshit and high on results.
Why weights? Stronger people, on average, live longer and with a higher quality of life. As you age you lose muscle mass and bone density, and resistance training offsets and even reverses both. It is also the one thing that makes people truly strong, unlike cardio or endurance (what Rippetoe calls LSD for long, slow distance), which have the added drawback of much higher injury rates.
Rippetoe would be the first to tell you that's not a surprise because people who have been getting really strong for hundreds of years have used the same basic logic: to increase functional (i.e. useful in the real world) strength use barbells and plates, concentrate on a few basic lifts that engage the body as a system, add weight every workout, and eat and sleep adequately to support growth. Lather, rinse, repeat. No need for Crossfit, P90X, Pilates, Barre, intermittent fasting or any of that other tripe. Do not use machines. Do not do curls or single-leg anything.
I've been following what Rippetoe calls the novice linear progression for 14 weeks now, and after starting with just a 45lb pound bar my lifts have progressed, as predicted, in a roughly linear fashion: squat 295lbs x 5 reps x 3 sets, deadlift 265lbs x 5 reps x 1 set, bench press 215lbs x 5 reps x 3 sets, press 135lbs x 5 reps x 3 sets, and power clean 135lbs x 3 reps x 5 sets. All of these are way beyond anything I've ever achieved on any other program, and this for a 40-something-year-old with a twitchy back.
The hardest part for me was eating and sleeping. Sleeping because of my three year old, and eating because I don't have that big of an appetite and a gallon of milk a day (GOMAD baby!) is just too much; I eat normally and drink an extra half gallon of whole milk every day. My starting bodyweight was 175lbs, with about 14 percent bodyfat. I'm now almost 200 pounds at about 18 percent bodyfat. So I gained some fat, but mostly muscle, and that's just the way it is: you can't get stronger without getting bigger, and that means heavier. As they say, if your abs are showing, you ain't growing.
Rippetoe can be over the top sometimes. He says things like, "The adult male weighs 200 pounds." Honestly it was hard for me to get past the first two paragraphs in Starting Strength where he asserts that physical strength is the most important thing in life, a rare instance of him confusing opinion with fact. But the fact is if you're interested in training strength this is the way to do it. Buy the books. Read them. Re-read them. Read the forums on www.startingstrength.com. Read his articles on T-Nation. Buy the DVD and refer to it often. For a total investment of about $60 you will have the absolute best available information on how to get stronger.