Your first goal must be to maximise satellite coverage. Countries with satellites give you money, engineers and scientists and continents with all countries covered give you a bonus ability. Most importantly, satellites detect UFOs on abduction missions. Abduction missions force you to choose two countries to increase panic so you want them to go away in a hurry.
Prioritise satellites and uplinks at any cost. Just don't launch them until the afternoon before the Council report in case any countries are in panic mode. Launching at the last moment can bring them back from panic and prevent them from leaving when the report comes through. Three uplinks and a nexus arranged in a square will give you full coverage. If some countries do leave the project before you get full coverage you might not need them anyway.
Sell anything you don't need (and stuff you do need if that's what it takes) to fund your satellites. You also need at least one workshop (for the extra engineers), and one generator to start building uplinks. That means you should choose the country which offers engineers for your first abduction mission.
Your dudes suck at first. They have bad aim, bad armour and bad weapons. They're just cannon fodder in the early game. Focus on preserving and promoting anyone who somehow survives long enough to reach Squaddie. Sacrifice everyone else to meet that goal. Once you start getting ranked-up guys things start to get easier. Buy the officer training school upgrades ASAP. As soon as you don't need money for satellites start to buy SCOPEs so your dudes can start hitting stuff. Research and build weapons as soon as you can but only research things which show their completion time in red if there's nothing else available to research.
Carapace and Skeleton armour can probably be skipped. Get one or two Carapace suits if you have some guys you really don't want to die while you wait for the better gear to become available. Give these armour types to these guys in this order of priority:
Assault: Ghost or Titan if you don't have Ghost yet
Sniper: Archangel or whatever no one else is using