Sorry haven't read the previous replies, but my story is much the same as yours. I am 5'2" and weight almost 13 stone, coming on for a size 16! Now in all honesty the diet was the first thing to change, and I lost about 2.5 stone (dunno if you're male or female, but coming off the pill probably helped too

). Anyway, I then took up running in the January (couple years ago now), and definitely definitely by July I was a size 8, 9 stone. BUT I was going to the gym atleast 3 times a week to start off with and slowly phased into running 5 days a week and a long gym session once a week, and then chucked in bouldering 3 times a week and cycling to and from uni (you could say, once I got going there was no stopping me!). In all honesty, it really takes quite a bit of time for you to really notice any real change happening, or atleast it seems like that, and you really have to stick at it, but once it gets going I'd say it happens quite quickly. Another thing is that you really shouldn't be too preoccupied with your weight and should just go with how you feel! Like you said, lean mass is heavier then fat, you'll might even find you put on weight before you lose any. So if your clothes are feeling looser and you feel better.. then that's great! That's the true signs
It is very important not to go toooo crazy though, like I have just seen above, it is very good to treat yourself! You'll resent it if you don't allow yourself the odd treat. Hell, I'm trying to lose my xmas pounds, but I still allow myself the odd bit of dark chocolate (mmmm *drools* greens and black maya gold...)! And I eat cheese quite a lot, but yeah... it's just moderation. If there was one bit of common sense advice about nutrition it would be "everything in moderation"... and if anything it's the highly processed carbs that will make you pack on the pounds, although obviously fatty foods will do it too... so first try switching to brown bread, rice and wholewheat cereals (they fill you up for longer too!) and try to
decrease any REALLY sugary foods, and instead of having a huge handful of grated cheese on pasta or something, just put a sprinkling over it... you'll still be able to taste it. I'd have to say cheese is my biggest issue though, I love it in all its forms! But then again, if I don't eat it that often it makes it taste EVEN better!! I haven't had pizza in ages actually... *licks lips* heh.
Anyway, all in all it's great what you're doing, and highly achievable, me and many others are proof of this, but I won't lie... it does take will power... but like I said, allowing yourself a little means you'll be able to resist a lot!
(sorry for the long rant!)