The first time I started working out it was with weights doing a push/pull routine (I think that's what it's called) -- a chest/back day, a biceps/triceps day, a legs day, and a shoulders day. The workout never lasted more than an hour and it worked well. I ended up gaining about 4 pounds (I'm about 5'11" too, went from around 170 to 174) in two months and dropping my body fat from around 12% to 8%.
Now I'm doing an all-body-weight routine as outlined in John Peterson's book
Pushing Yourself to Power. It works well because you don't need all sorts of different equipment, you can do the exercises anywhere and anytime, and it involves a lot of deep breathing which really does give me more energy and feels really good. While there are quite a few bodyweight training books out there, this one contains step-by-step pictures of the exercises (of which there are very many in the book) and the regimen Peterson suggests is quite reasonable and specific. The book seems at least partly intended for middle-aged people because the exercises are a lot easier on the joints, but I'm 24 and I'm enjoying it a great deal. Peterson also provides a lot of good nutritional advice which is a nice plus.
The basic rules of good nutrition, very basic outlines of things you should aim for, seem to include eating smaller portions more often (about every 3-4 hours), getting rid of white carbs in exchange for whole wheat/whole grain foods (white rice -> brown rice, white bread -> whole wheat bread, white pasta -> whole wheat pasta), and eating less fat, less sugar, and fewer processed foods.
When I started working out that first time I was a lot more serious about my nutrition. I would usually eat about 4 oz. of lean grilled chicken breast on whole wheat bread for a lot of my meals, which got to be pretty tedious after a while but it paid off. But there are other foods you can eat, too. Tuna is really good for you as well, as is lean turkey breast and even lean steaks. You can replace the bread with brown rice, whole wheat pasta, or even spinach as I've seen some people do.
So you may want to look into purchasing the Peterson book, which costs around $20 online. If you get it, I suggest buying the spiral-bound version since it stays open while you're exercising. I made the mistake of getting the regular binding which has been a bit annoying. Just remember that working out requires a lot of your own motivation, and the bodyweight-only exercises that you do at home sometimes require even more motivation. You have to want to get in shape and be willing to work for it to make it happen.
Two good websites you should visit are
www.bodybuilding.com and
www.johnstonefitness.com (focuses on weight training to lose weight). They'll give you the more traditional weight-training approach to fitness if that's what you end up deciding to do. Bodybuilding.com is also good because it has its own searchable/browsable exercise database complete with short videos that shows how to perform the exercises.
Good luck, and if you have any questions ask them -- there are a lot of people here who are a lot more knowledgeable than I in this area and who helped me out a great deal when I first started to work out.