Strength Training without free weights?

Okay, so in addition to a vigorous swim routine and some hard cardio here and there, I've been playing with the idea of also trying to tone up a little bit (I don't want to be a female Dwayne Johnson though).

Issue: I'm unemployed and broke. I work for my boyfriend for free at his store so I don't feel so horrible for being dead weight. I use what I have, and what I have isn't much; my apartment provides a pool, treadmills, elliptical, a bike machine, etc.

There are weight lifting machines, but every single strength training guide I see regards to doing squats with barbells (I will NEVER do this, you have no idea how clumsy I am), free weights, etc.

The machines I have to work with, I honestly don't even know their names. I'm very new to this concept so forgive me. There's a leg lifter that I've also seen people using to do crunches, that arm machine where you pull the two things forward, and another machine where you pull a thin bar downward.

I'd probably be focusing on the arm machines, my thighs are already way bigger than they should be, and I am *pitifully* weak anyway - like, I can't even go bowling. From what I gather free weights are more effective, so I'm just assuming I'd need to work longer/harder, yes? I have a lot of time to myself so the length of a workout doesn't deter me much.

I have a doctor's appointment today that was originally for something else but I'm going to ask him about how I can improve my diet more than I already have, maybe add more protein, etc, but I don't know if my doc would know about the inner workings of strength training better than a fitness site would, lol.

I've also seen that there are two types of training and I forget their names but one basically makes you beef up (which I don't want) and the other helps you lean up (which I do want). All the reading I have been doing has not been explaining the difference between the two and I've found no clear answer on how to prevent accidentally building mass when you're shooting for lean muscle.

If it helps, I'm currently 144 lbs (goal weight of 115), 5'3, and 24. I seem to carry my fat in my stomach, thighs, and butt. The only good thing about my weight gain is my boobs got bigger, LOL.