Asphalt. If your goal is to train for a race, then at some point (usually after ‘mastering the grass), your feet must meet the asphalt in order to prepare yourself, since most races happen on the street. Asphalt lowers the tension on the heel, and it has shown to be a pretty great running surface, as well.
Keep in mind that running on the streets is not safe. Make sure that you wear bright colors with reflective strips that will keep you noticed. Also, lose the headphones so you can increase your awareness and reduce the danger.
Concrete. Those of you who live in big cities will find miming on sidewalks to be the safest and most convenient option. However, it is also the worst one. Know that concrete is one of the hardest surfaces and can, therefore, increases the stress in your joints and muscles. Although good shoes with proper cushioning can help, try to limit the running time you spend on the sidewalks.
Treadmill. First of all, know that running the same distance on a treadmill and on a real surface is not the same. Treadmills also pull you as you run, which makes the whole process easier and allows you to run a long distance. Running that same mileage on asphalt or grass will be trickier. Now, the treadmill as a running surface is great if you have suffered an injury or want to reduce the stress on the muscles. However, not being able to observe the surroundings as you pass them by can be boring and quite discouraging.
Hills. Although the climbs are really determined by the area itself, beginners should try to avoid running up and down hills and climbs when possible. Running up a hill requires a great physical condition and running strength, which you, at this initial stage, lack. Running down a hill may look like a better choice as it can increase the pace. However, that is only short-term, since the downward slopes put too much stress on the joints.
So, which one to choose? Start with grass, avoid the hills where possible, and then mix the other surfaces in. Having a running route is great, but running on the same surface all the time, not so much.