help me strengthen my core and track my workouts.

With regards to strengthening your core, I would start out with some planks--I've really been noticing a difference after I started doing them. As for Android apps, I use Fitocracy on the iPhone, and they're coming out with an Android app soon.

Have you considered http://www.youtube.com/watch?v=huVujjfzphI? They're the big fundamental movement in both http://startingstrength.wikia.com/wiki/The_Starting_Strength_Novice/Beginner_Programs and http://stronglifts.com/stronglifts-5x5-beginner-strength-training-program/, both of which are programs that emphasize full-body exercises which will absolutely help you gain core strength. It is doubtless that several other people will come into this thread to try to convince you that Starting Strength is a great program, and that is because it works splendidly for people.

I also had some back issues in my early 30's, which pretty much disappeared after I started going to a gym. The first gym I ever went to was my local YMCA, which had a few free sessions with a personal trainer; here's what he told me to do. * 30 minutes of cardio, 3 times a week. The bikes and the rowing machine would do the trick. The rowing is also good for your back, as a bonus. * Then twice a week, there are 5 machines I visit once each, doing three sets of ten lifts/pushes/whatevers: first the http://fitnessanddefense.com/wp-content/uploads/2011/04/Leg_Press_Machine.jpg then a http://ecx.images-amazon.com/images/I/31VXA7dfcRL._AA300_.jpg then the http://www.gtechfitness.com/images/products/detail/Magnum_2021_Lat_Machine.jpg machine, and then I either use the machines that work the biceps and triceps or I just get some little dumbells and do it that way. * I finish up with about 3 sets of 15 crunches, and call it good. I technically could be doing more, but doing as little as that has kept my back totally pain-free for four years and counting now. Any staff member at the gym can show you the proper way to use the machines. Don't worry if you have to start off with only a tiny bit of weight; I do, and that's just that. It's enough to make me feel like I'm doing something, and I'm not looking to get ripped or anything, I'm just trying to stay relatively healthy.

It's probably not what you want to hear--and it's advice you'll need to be very careful with--but my back has never felt better than when I'm squatting and deadlifting on a regular basis. I've had off-and-on back pain for quite a few years now, but never while I'm lifting regularly. (Except, of course, when I was careless with the lifting; you should take it very slowly, pay extra attention to your form, and maybe find a competent trainer to show you "how" to do these lifts. Emphasis on "competent.")

Are you open to working with/can you afford a training session or two? I have taken classes off and on over the years and through those session I can mix and match a lot of different exercises now. From those sessions I learned that I was doing a lot of exercises "the wrong way" so if you have the privilege of a session or two, I would recommend it. On another note, a lot of gyms these days have 20-30 minutes circuits of "machines" set up near the cardio floor area. That could be a great way to slowly build up your strength and endurance when it comes to weights in a facilitated manner (and as others above have noted, staff should help you use the machines properly).

ExRx (Exercise Prescription) is one of my favorite resources http://www.exrx.net/Beginning.html http://www.exrx.net/Lists/ExList/WaistWt.html with bodyweight exercises on the right.