Working out has all pros and no cons, trans or not trans. I can't recommend enough to workout not just for your health but to pass in everyday life as the dude you really are. When I was pre- T weightlifting was the magic ticket. Before it I was always being called "she" but when I started lifting iron and gained some size it was "Sir" from that day forward.
When starting any new program you should take nutrition under advisement. Good nutrition can make or break any chance of your body making the gains you want. That means getting a trash bag and throwing away all that CRAP you call food and replacing it with fruit, veggies, lean meats, wheat breads, and buy yourself a big ole tub of protein powder. Protein is very important to build muscle, you can not build muscle out of cheetos and soda. To get big you got to eat big, that means 3 meals a day and 2-3 snacks a day. Your main meals should consist of protein ( some kind of lean meat), carbs ( veggies or fruit), and fat (avocados, fish, olive oil). And try to eat at least 1 gram of protein for every pound of body weight.
Okay, now to actually working out and breaking a sweat. You should aim to workout at least 2-3 days a week, in the perfect world you should really workout 6 days a week with one rest day. When I say 6 days a week I mean alternating from weightlifting and cardio. For example:
Week 1:
Mon : Upper body
Tues: 2 mile run
Weds: Legs
Thurs: play basketball with the guys
Fri: Upper body & Abs
Sat: Swim
Sun: Rest
Week 2
Mon: Legs
Tues: 2 mile run
Weds: Upper body
Thurs: Bike ride
Fri: Legs & Abs
Sat: 2 mile run
For cardio do whatever gets your heart rate up and makes you sweat. Since we are trying to build muscle running sessions should be not longer than 20 - 30 minutes but keep the intensity high enough to make it tough to chat to your little gym buddy.