Hey, it is good you are thinking about health, I am too lately. I think too, if you are someone, like me, that has used lots of time most days on the computer it is good to take a short time to stay healthy. For example, I sometimes can spend many days of the week for so many hours on the computer, so you should think: if I am on computer for sometimes even six+ hours a day! it is good to take 30 minutes/1 hour of that time and do a light exercise, because if you did that almost every day for the past year, you would see big results/difference!
So almost everyday of the week, at least three days a week, try to do some light exercise, even just walking. If you walk for 10-20 minute straight, it would be a workout! and I recommend, if you never have worked out a lot, to start very slow, you don't want to immediately start "pumping the weight," you need to do light exercise like walking, stretching, very, very ,very light cardio exercise to build up your body to be ready for more intensive working out. Even pushups and situps could be too intensive depending on how out of shape you are and if you have never worked out/have begin to deteriorate you muscle mass even slightly.
I recommend after getting used to walking/stretching consistently for at least a month or two, start trying to do things like stretching and preworkout light cardio (jumping jacks, running in place, etc) and then do some push-ups and sit-ups.
After if you are trying to build muscle = lift more weight in dumbbells and do less reps.
If you are trying to slim/lose weight = lift less weight in dumbbells and do more reps.
Never try to do more weight with dumbbells than you are able too, you should never sacrifice your "form." It is more important to execute a proper form that does not strain your body so you do not build your body the wrong way.
I recommend using dumbbells, free weights workout more than machines because free weights will work your stabilizer muscles and machines will not.
I think most basic and necessary workout, after you prepared your body for this kind of "intensive" workout, is dumbbells you are comfortable lifting (even 5-10lbs dumbbell is fine, you DON'T need to lift lots of weight!) and doing basic workouts each day like a day for biceps/back, a day for chest/shoulders/tris, and a day for legs, basic dumbbell movements can work all of these muscles and even push-ups, sit-ups and laying on the floor lifting up your body can work out triceps, google for many different workouts, and always do it with proper form, if you don't do the right form, there is no point, you will mess up your body. and of course, breathing is very important.
and like others say, aside from working out, I know it is hard to always "eat healthy" just try to consume more vegetables whenever you can, fruit is good, but overdoing fruit, even natural sugars from fruit, is not as good as eating the fiber and nutritious vegetables (dark green vegetables very healthy). You can still eat whatever you want, just try to make it less "junk food" and sometimes more healthier food so it is not always bad food all the time.
again, very important I want to say, if you are out of shape and have not worked out in a while, or ever, do not start working out heavily at all! Do walking ! Build up your stamina, become more flexible with stretching, practice good breathing.