Second: stop worrying about fat, start working on strength. Build up some base muscle, 15-25# of gains, then reassess your goals. That's probably a 12 month cycle here. I'm a big fan of 5x5 programs (Stronglifts 5x5, Rippetoe's Starting Strength), but find something that works for you.
You've dropped 120#. You've probably lost a fair amount of muscle in the process, especially if you weren't strength training while cutting. You also probably have at least some excess skin, which will tend to look like flab. At 120# loss, most of it should resolve on its own (the body is very adaptable), though it may take a while (give it a year or two).
Go for a 9-12 month mass-gaining program. 5x5 as suggested above, until you can squat 1.5x bodyweight. At that point you've got a solid strength foundation to look at further goals.
As a long-time cardio athlete (swimming, cycling, hiking, rowing), it's not as essential to fitness as a lot of folks would have you believe.
First: strength training itself is a pretty good cardio workout, especially if you're working with shorter rest intervals. As you progress with a 5x5 program you'll be resting 3-8 minutes between efforts, but at 2-3 minutes you're still going to keep your HR elevated for most of your workout.
Otherwise: I try to get 1-2 HIIT sessions and a third long-distance effort in weekly, if possible. Depending on your age and training intensity, rest is actually going to be more useful than additional time exercising.
Either cardio after weights, or in separate sessions. I split my training days between cardio and weights. It's usually been a 3x weekly strength session (M/W/F), with cardio on Tu/Th/Sa. HIIT is Tu/Th, LSD on the weekends. One rest day per week, at least.
Keep it up and keep us posted on your progress.