Warm up Cardio before lifting, cardio after?

So I have recently started lifting weights as part of my weight loss/inch loss goal. I am female, 27, 5'5 and 157 lbs. I am hoping to get to 140 (or a size 6) at some point here.  I have already lost 63 lbs starting out at 220 lbs of February this year. All done by counting calories, lots of cardio and a free day once a week.

I added weight lifting because I want to maintain the muscle I have, increase my metabolism and even when I go to maintain calories I would like to  get smaller by reducing body fat and increasing muscle.

What I have been doing is running/jogging 1 mile (so 9 - 10 minutes) before I lift weights, then I will lift for 20 - 30 minutes and then go on the bike for a while (20 - 30 minutes ) or something like that, 3 times a week. Days that I don't lift I will just walk at high incline, elliptical or some other sort of exercise to keep me active and get a deficit. 

Is any of this detrimental? should I just go to the gym, lift first and then run 1 mile? What works best for my goals stated above?

I lift 3/4 times a week, I try to lift heavy and add weight every few days to challenge myself. I am getting stronger and lifting more now then I did when I started a few weeks ago. I do cardio to increase my calorie deficit and also because I am in a miles competition with friends so I need to get miles for my team.

P.S. Realize I didn't say anything about my eating habits, not sure if it matters. I eat at a - 200 to - 800 calorie deficit 6 days a week.(1,300 - 1,800 calories depending on activity which is USUALLY high so my calorie intake is USUALLY 1,500 - 1,800) Sunday is a maintinence or slightly over day. I have been losing pretty steadily with a few plateaus as I get smaller but nothing over a few weeks long.

That's not a bad routine, and it can certainly work.. but running only "warms up" your lower body, so i would do some sort of full-body warmup, like the elliptical or rower machine, for about 5 minutes.  Then do a warmup set or 2 for each of the major muscle groups (legs, chest, upper back) before lifting heavier.  

A good, proven routine is a full-body lifting workout (as opposed to split workout), doing mostly compound exercises (as opposed to isolation exercises), done 3 times a week, with cardio done on non-lifting days. 

That's usually what I do 3-4x a week. I warm up 15-30 minutes of cardio, and if I want to, I'll do some more cardio after my full body weight circuit. The other days I do cardio 45-60 min or so. I've seen results from it.