There's no easy instruction to this game. You have to expect to get your ass kicked and work with what you're given. The start of each game has subtle differences that will effect your immediate progress, planned builds etc. It's impossible to plan for every eventuality. So I can't give you a step-by-step process.
I like to complete games to the best of my ability; but I have to admit defeat in XCOM, I have to try and scrape by. This is not a game for perfectionists. SAVE OFTEN!
The early game isn't too hard. Here are some things that you might consider:
I try to manufacture satellites early, so they are ready when I establish communications links. It gives better retention of council members/countries/funding. You should only place satellites in the continents where your base(s) are located. Otherwise, your satellites will fall prey to enemy UFOs. You can't protect everyone, unfortunately.
Don't be frightened to use rocket launchers and grenades. Taking out multiple enemies efficiently increases your survival rate. Even if it hurts your research resources.
If you find it difficult to balance resources in the early game, start in Africa. It gets a substantial monetary supply buff. You can concentrate efforts on acquiring scientists and engineers.
Sell items on the grey market for additional funds. Money makes things easier and faster.
Always move into cover. It is better to make shorter steps with adequate firing cones from nearby units. Don't run long distances where other units cannot give fire support. Always set up "over watch" positions to intercept alien reinforcements. This is especially useful on rescue missions, or bomb disposal missions. Aliens will drop reinforcement atop buildings and vehicles. Be ready for them. Try to "peak" corners from distance. Don't run into a building to get a better look. Blow a hole in the wall for visual assessments.
I do believe that armour and weapons upgrades outweigh the plot line. Try to improve your soldiers and increase your squad size early. You will have to complete multiple tiers before you get anything substantial. Do not purchase the first set of armour that you research. It is far better to spend your resources on the following armour upgrade. Otherwise, you will not be able to afford the superior armour when you need it most. In short, you're only completing certain research projects to gain access to the next. Not every upgrade is worth the coin. So research far outweighs engineering - you shouldn't saturate your engineers on too many build projects this way.
Heat ammunition for heavies is especially useful against armoured, cyborg/mechanical units.
I happen to like the assault class for flanking routes. They can fire in the "yellow zone" with the run and gun ability. But you make that move at your own risk. But I tend to be offensive and eliminate enemies before they can eliminate me.
My ideal squad is 2 assault, 2 support, 2 heavies. The support should carry the 3 medic kit upgrade, and you would do well to give them more movement points.
Aircraft upgrades are especially useful for intercepting larger space craft in the early game. Larger space craft net you more research resources/materials. Worth the risk, in my opinion.