Where should I use my speciality points?

It depends on how you want to improve your performance. Some areas help you get more honor points (which help you level up and get more speciality points quicker) and others give you advantages in any combat for doomsday war. A recommended approach though if you are starting out is to spec into the Blue section and try to reach the 4 larger circles at diagonals from the center called Construction Master. These allow you to build more honor buildings (virus center, production center etc). If you build more virus centers then you can increase your immunity faster which allows you to occupy higher level plots. This will help you advance quickly.