Combat: Go slow, use overwatch a lot. It starts off pretty easy but the difficulty quickly ramps up as the game proceeds so always try to deal with whatever enemy is onscreen on your own terms. Also, if you're on your last character of the turn don't push forward, just overwatch.
World Map: Always keep a few satellites in reserve, make sure you don't overspend on anything - try to have an idea of why you're buying what you're buying so you don't get caught short. Try to keep a watch on your soldier pool aswell, having enough to keep playing/how long it'll take the injured to recover.
The challenge on the world map is mostly about balancing your terror, and trying not to have any country drop out, if you think a country's going to drop out at the end of the month (if they're on 5 panic bars) then you can always launch a satellite over them.