Hey Redsky,
So you say you have come across a facehugger lol? Yep, these are annoying, though very fragile. Same as with Reapers (the other guys that can zombify your soldiers) you just need to keep your distance and use vehicles for spotting - when you spot them, you can withdraw the tank and use the snipers/rocket launchers. Also, I use a lot of incendiary grenades as an area denial means - many aliens will die walking through flames, but many will try to walk around it and gives you valuable time. Honestly, in some longer missions, I just bunker up - drop smoke grenades in possible routes and try to lure the enemies out.
And yes, you need to take it slowly, create a parameter and methodically push it forward - this way you will always have your enemy in front of you, so no nasty surprises will hit you from behind. There is no best method, it will have to come with experience I am afraid. Also, make sure you have a diversified arsenal, all laser/all ballistic/etc usually means that you may come across an enemy that will be veeery difficult to kill.