Lost weight with just dieting, just started working out so a few questions.

Hey,
I'm new here and first of all this website has got to be the most useful tool I've found on the internet. I almost got Insanity but with help from the website I'm making my own routine. I'm 20 years old, approximately 5'6 and weigh about 160 pounds (seems to fluctuate between 159 and 162) Since November I've lost about 20 pounds through intense food reduction (I was about 185, give or take) but I did very little working out through that time. Anyway, enough introduction, I've still retained a decent amount of fat especially around my stomach and thighs and my stomach has a very 'loose' look to it. For me, I don't care as much about my arms (although that would be nice), I care a lot more about how my body looks (I was quite heavy when I was younger). After using the personalized workout plan I came up with this routine.
Sunday, Tuesday & Thursday: pushups, dumbbell flys, pullups, dumbbell rows, crunches, barbell curls, dumbbell french press, side raise, alternating dumbell press,lunges. 8-15 reps of each, and 3 sets of each. I follow that with a 20 minute jog around a track. ( I read to keep this up until I can do 5 unassisted pull ups)
Monday, Wednesday, & Friday: I do HIIT, 5 Min jog, 6 Sprint Intervals - 30 Seconds each, 6 Rest Intervals - 90 Seconds each, then I'll jog 5-7 minutes to warm down (to bring it to 20 minutes.
Saturday is my day off, so I just do a 20 minute run on the treadmill.
My nutrition right now is as follows: I usually have a breakfast bar in the morning ( I am usually in a rush to get to class) Fish for lunch, and grilled chicken for dinner with vegetables spread out sporadically (I'm not having enough vegetables, I know. I'm working on that, but being in college, their sometimes hard to get a hold of) I'm drinking a lot of water (I don't walk past a water fountain without drinking) and on my workout days (weight lifting and such) I'll drink a bottle of chocolate milk afterwords. So I guess my question is, am I doing (at least for the most part) the best I could be for my goal? Any advice? And also, as I'm supposed to be doing 3 sets, which is better; going through the whole workout routine in order 3 times (after I finish the lunges, start at pushups again, 3 times) or should I be doing 1 set of pushups then rest, then second set of pushups then 3rd and then move on? I appreciate the help as I'm pretty new to going to the gym (only about a week now, I did used to run 2-3 times a week and did pushups, sit ups and pullups twice a week, but I fell out of it and haven't done it seriously for almost 8 months) Anyway, thanks again.

Gaining muscle is less of a priority to me. I'm more interested in losing the extra fat around my stomach and getting visible abs and focusing on gaining muscle a little farther down the road. I have access to a gym most of the time (not on weekends, then I only have a few dumbbells, a pull up bar and a treadmill ) so I have most equipment available. Would your suggestions be a better option than the ones suggested in the personalized workout? I appreciate your help, thanks.