Hi Adrian! Welcome to the forums! I'm not an expert on running by any means but I'll give you my opinions for what they're worth!
Firstly, running surfaces. Whilst RW mag would have us all believe that every runner lives 30 seconds from a running track it's not always the case. Therefore, you need to make the most of what you've got available. If you can, run on the road rather than the pavement - tarmac is very slightly more forgiving than concrete - and saves the constant up and down of kerbs and driveways. Grassland isn't necessarily much better for your ankles and knees unless you can guarantee it's flat because the uneven surfaces can twist your joints into awkward positions.
Obviously the best place to run is on a track - or failing that the treadmill. In this weather, however, you really don't want to be stuck indoors so I'd save the treadmill sessions for once a week and use them for speed or interval training.
Onto weight training, from what I know a lot of runners do nothing but running but there are advantages to doing a couple of weights sessions in the gym each week. Strengthening the quads and hamstrings on the legs will of course help your running, as will calf raises. And strengthening your arms will help as you use your arms to propel you along whilst running. In addition, working on your abs (stomach) will improve your posture whilst running - have I convinced you yet?!
Anyway, see how you get on! Keep your training steady - don't increase your mileage by more than 10% a week. And if you haven't done so already, get yourself to a specialist running shop and make sure you get a suitable pair of trainers for running outside.