You can lose fat and gain strength at the same time when you're new--provided you are consistent and intelligent about what you're doing. The longer you train and more specifically the stronger you get the harder it is to lose tons of fat and improve strength at the same time. For newbs it is pretty easy if you stay focused.
Eat more. eat 4-5 evenly spaced times a day, eating about the same amount of food at each time.
I would recommend walking every morning for about 30 minutes at a pretty quick pace. It won't interfere with your weight training and it will help burn calories.
The key for people in your position is usually a variation of the following:
focus on weight training consistently and hard
focus on eating consistently and evenly spaced out
focus on low intensity activity that burns calories but doesn't drain you. Hiking, biking, walking, swimming, etc.
That's the entry level recipe.