5'9" is a good height. Not too short, but not tall enough to make push ups and bench pressing a real struggle. If you have access to a gym in your school (which I think most colleges do) they get ready to make it your home. All it takes is 1 hour a day, 5 days a week. You can go after your last class of the day, or if you have late classes some time where you have a good 2 hour break.
Don't be embarrassed to start with body weight and just bare bars. The most important part is going to get the technique rights. Though you will hear you need to lift heavy to get big, it's useless if you aren't doing the moves right. And it's a lot easier to learn the moves right when you work with lighter weights. Look up videos and honestly, if you have any questions don't be afraid to ask someone something. Plenty of people won't mind taking 30 secs out of their day to demostrate something. That's how I learned to deadlift, it's not always the same watching a video as seeing it in person.
Also, once you start to go heavier always get a spotter when doing a potentially dangerous exercise until failure (bench press, etc.). It also makes for a more effective workout when they help you push out an extra 3 reps.
I'm sure you'll find plenty of exercises, work outs and routines online. I like using exrx, they show you exercises for the muscle group you look up and by equipment you are using.
Diet is also a big part. You can buy a decent protein shake and shaker bottle. You're going to want to eat a good amount of protein (natural and supplements), some carbs, and fats (good fats though). For breakfast you get have cereal (5g protein per bowl) with milk (another 8g), yogurt (12g protein for greek yogurt, coconut, key lime, orange creme and pineapple are my favorites), bananas (vitamins and potassium). Lunch can be whole wheat or potato bread with deli meats (turkey, chicken breast, salami) or tuna. Dinner can be brown rice or whole wheat pasta with beef, fish, or chicken (or pork every once in a while) and a side of vegtables or a salad. You can snack on nuts or trail mix through out the day or eat peanut butter sandwiches. You're also going to want to drink plenty of water though out the day, but not a lot with your meals or when working out. And you can start taking a multivitamin in the morning. You can take a protein shake right after working out, and if necessary you can take one in the morning.
I started lifting sophomore year of high school, coming out of breaking my arm twice in two years. I took two years of weight training and by the time I was in college I was 5'6" 155 lbs bench pressing 225 lbs. It hard at first and it sucks, and you're gonna be sore for days after lifting, but soon it starts to get funner, and you start adding more weight, and noticing improvements, and before you know it you're addicted. I've gotten a few of my buddies into it too. Give it 6 months, you're gonna be real have you stuck it out. Good luck and if you have any questions message me.
P.S. also, don't neglect your legs. Bodybuild I went to school in the Navy with told me that doing legs releases hormones which helps get your upper body bigger too. That what you hear Mark Wahlberg talking about in the end of Pain and Gain "weak quads". Squatting and deadlifting are fundemental workouts. Other good ones are chest/tricep dips, bench press (flat, incline, decline), pull ups, curls (bar and dumbbells), rows, overhead press, and shrugs.
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