I'm playing on genius (probably seem to be a newbie among all the guys playing superhuman), and the third UFO that came to earth was a sectoid battleship, that attacked my base
I have even captured a commander, but he died because my alien containment was few days short to finish building...
I always was on low cash, because I think that banked money is wasted money. I spent as much, as I could if it didn't get me into loans.
what I've done is:
a) get some good soldiers -> I prefer reactions over fire accuracy, and that made me profit really well. I just hired some soldiers, fired everyone below 45 reactions, and hire some new guys. I quickly got some nice guys for the start with reactions above 50 each, and not bad shooting skill. I took 8 of my best soldiers to the skyranger, counting their value as 3*reactions + fire accuracy
b) took rifles for each of my guys except the person with the rocked launcher
c) got laser rifles equipped - this is almost all I actually needed so far throughout the whole game
d) the better armor you have, the easier it gets
e) I always used the least powerful weapons that do the job - you need to get more hits to kill the aliens, and have more chances for reaction fire, skills go up really fast. an exception is when my base is attacked, or when I attack an alien base.
f) I've made 2 additional bases quite quick, but I doubt any of them in the first month
g) at night you need tons of flares ( I had 3 per soldier )
h) grenades are a blessing. smoke grenades, high explosive and proximity grenades are really helpful, but I always used them as a last resort (except for smoke grenades, which are helpful if you don't want to get killed while getting out of the craft. when your reactions are nice ( for genius this is like 85 and more ) you don't need the smoke's anymore.
the rest I've done probably as everyone else. in my game it's july, and I have had a score like 13k.