-Don't worry about the weight so much, cuz you'll almost certainly gain weight as you add muscle.
-Do at least a few minutes of cardio before you lift. Getting your heart going will help the rest of your body, and it will also loosen you up some before lifting. Also, more cardio = more fat burned = weighing less. Yes, I know it's boring as shit.
-Stretching is good. I don't stretch excessively, but I do like to try to loosen up whichever body part I'm about to work. Especially knees, but then I have shitty knees.
-Drink plenty of small sips of water. If you start feeling thirsty you're probably somewhat dehydrated already.
-Breathe. Take note of yourself breathing, and get into a rhythm of breathing/lifting. Also this may seem like a pointless thing to tell you, but it's much easier to breathe deeply through your mouth.
-Don't neglect your legs. Your ass/legs are your biggest muscles, and therefore your best fat-burning tools. Leg exercises aren't as fun as upper-body stuff is (for me at least), but it's gotta be part of your workout lest you end up like this:
Red Stripe "Legs" Commercial-You might consider hiring the services of a trainer for a couple of sessions, to familiarize yourself with the various free weights and machines, and to be shown how to do more different exercises than you'd probably think of on your own.
-Compound exercises are particularly good for adding muscle and burning fat, you're utilizing more than one specific muscle at a time, and your heart rate will be higher than a simple isolation exercise will get it. A fairly easy one to start off with would be hammer curls into shoulder press.
-I like to do circuits of different exercises, interspersed with short sprints on the treadmill. It's pretty tiring, but it keeps your heart rate up.
-Eat nothing but super-healthy food.*
-Don't drink a whole bunch of booze.*
---
*My failure to follow these last two steps is why I'm a pretty strong, fairly fit, but cuddly 230, instead of some kinda lean, mean, muscle machine.