New to this...where do I start? What can I do?

Summary/basic info: I'm female, 5'9 and approx 220lbs. Age 27. Large build. Very healthy diet (no sodas, little sugar, little to no fast food, little to no candy and desserts, lots of veggies, grains, lean meats.). I signed up at the Planet Fitness gym a week ago and am going every other day for at least an hour (I'd do much more, I love it there, but my bf is often exhausted after work and that cuts into the time I have.). My apartment is also small, so working out at home isn't much of an option. Winter is coming soon, so my outdoor activity is very limited too.

Sorry if the forum post ends up being long, but I'm hoping that my background can be useful in answering some of the questions I have. I'll be posting as many as I can think of....which will likely be a lot.

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Ok, so exercising has never been a part of my life really. I've always been active and healthy...I grew up on a homestead/farm, did physical labor jobs (woodcutting/hauling, carpentry, hauling slate, wrestling pigs etc) and have always been stronger and more fit than most average men I've ever met. Despite being overweight all/most of my life, I've always received a lot of praise from physicians about my unusually excellent health. No heart problems, no diabetes, no nothing (double negative, get over it. :P ).

I came to Pittsburgh in 2005 and have been here since. In the city, women don't do physical things as often as I was used to and I kind of 'fell off the wagon' I guess you could say. Desk jobs, etc. I've lost a lot of the muscle that I used to have and gained a lot of weight (due to my ex.). I went from 190/200lbs to about 285. I'm back down to 220 (after a period of extreme stress during the ending of my first relationship which ended in 2011. I stopped eating and was lucky to get 800 calories a day in me for at least a year.). I have been at around 220 for the last year, so I've begun eating again and feeling better.

I do want to lose more weight, so my goal is to burn as many calories as possible but I also want to build muscle (to, you know, tighten up my bat wings).

So far, this is what I've been doing:

Cardio to begin on the treadmills there. It's often for about 30 minutes or longer if I'm able to. I set it to the Cardio option and 2.8 speed. It automatically changes the incline for me, so it goes between 1.5 and 8.

Should I be varying the speed for best calorie burn?
Should I focus less on speed and more on the incline option?
I reach Target Heart Rate (machine suggests 155-160) in about 3-5 minutes (some days are better) of this. Is this too quick to reach my Target Heart Rate?
My boyfriend can be on incline 10-15 at a 3.0 speed and still fight to get his heart rate up above 120 (he's the same height/weight as I am. He's a nurse's aide so has had more physical work recently than I have.). Is that normal?

For strength training, I use the equipment that they have. I set the weight to what feels comfortable but gets very difficult to do around 10 reps or so.

I'm also curious about how horribly weak I've gotten. I don't even know how I compare to another guy/girl aside from my bf.

Here's what I did yesterday:
Leg Press: 16 reps at 220lbs. (needs to go up another 20lbs)
Leg Extension: 10 at 110lbs.
Leg Curl: 10 at 90lbs.
Calf Extension: 10 at 130lbs.

Upper Body:
Lateral Raise: 8 reps at 50lbs.
Fly: 10 at 70lbs.
Chest Press: 10 at 60lbs.
Pull Down: 11 at 90lbs.
Row: 10 at 70lbs.
Shoulder Press: 9 at 30lbs (personally, this is such a low weight, is this low compared to everything else? Should I really work on this?)
Bicep Curl: 10 at 40lbs. (I start having a hard time pulling them at this point, not due to pain, just can't anymore. Is that also normal?)
Tricep Press: 13 at 80lbs.

At what point do you suggest raising the weight to make it harder?
Should I be aiming for more reps at a lower weight? Like, 20-25 reps instead of 10-15?

After the Strength Training, we get back on the treadmills for a while longer. I really try to keep him on them as long as we can, but again, he's usually really tired from work to be on for more than 15 minutes.

So, more time strength training, less cardio? More cardio less strength training?

Any advice is appreciated. Questions are welcome if there's anything I forgot to cover.