I've yet to try Classic. Sounds like it should be a good challenge. Normal has been relatively easy on my 2nd playthrough (Game 8 though so I did restart it a few times as I learnt the ropes) apart from the glitches/bugs (mainly Floaters appearing out of the ground under/near my troops) getting troops killed.
My tip. You get the continent bonus for whichever continent you start in automatically. So, if you can, save coverage of it until last. In my current game I started in Asia and put my first satellite up in the US and went from there. But yes getting full coverage is my #1 goal. Once you have that you can worry about everything else. To that end you need to concentrate on Engineers first.