The normal range of testosterone levels for a man is 200-1100 ng/dL, and guys at the lower end of that aren’t gonna be bodybuilders any time soon, or ever, really. The range for women, on the other hand, is 15-70 ng/dL. If the guys who can’t build muscle most likely have three times as much testosterone as you, you’re probably not going to have to worry about bulking up unless you’re planning on taking drugs. Don’t do drugs.
Now, if you want actual out-of-gym strength gains, you’d do best to leave the machines behind and stick to free weights. Briefly, there are two groups of muscles in the human body: big ones, to move you around; and small ones, to stabilize your movements. Machines train the first but not the second, and so they’re not going to help that much when you’re trying to move something that’s not attached to a pulley. Stick with the machines too long, and you can actually detrain your stabilizer muscles and end up weaker.
So, upper body strength. In most cases where you want to be stronger, you’re going to want torso and leg strength to either assist or stabilize yourself. You also want a strong posterior chain (everything on the back of your body) because that’s where strength comes from. The six core lifts are the squat, the deadlift, the overhead press, the chinup/pulldown, the row, and the bench press, and they all address at least one of those concerns. Focus on them, add some assistance exercises as needed, and you’ll make gains quickly.
Your first goal is to learn to do the exercises properly so that you don’t hurt yourself. ExRx has good animations to show you the proper form. Krista’s site has a lot of really excellent information for women who are starting out a weight-training program, and I highly recommend it.
Just in case you’re curious, here’s my current strength-training program:
Day 1 (Tuesday)
Day 2 (Thursday)
Day 3 (Saturday)
Biceps Curls (pure vanity)
Despite the low number of exercises, days 1 and 3 are challenging full-body workouts. Day 2 is sort of a catch-all for other important stuff and a lighter day between the two big ones.