you can also upgrade your CR3 units into mechanized infantry, and all those rifleman just LOVE being mobile SAM or Sam Infantry to seal your own skies.
Marines: moving 7 spaces through enemy territory, you can send in some pawns onto forts, hills, forests and other areas where they will be annoying to deal with, the more pawns = the less responders to your SOD.
Air Force: Its actually better to bomb away cities you can't pillage in just yet or use them to bombard SOD's outside of cities. you can also destroy any forts they are hiding in.
Tanks: Not as powerful as they once were as they no longer have barrage. These babies can smash down any town or SOD. It is often a good idea to treat them like calvary because they get no tile defense.
Mechanized Infantry: Your best friends, they can both get a tile defense, and intercept air units. If promoted to CR3 from an earlier unit that is promoted up to one of these, your looking at a winnder.
Promotions: Pinch is pretty good. Really, the ones that give bonuses vs gunpowder and armor units are the best ones. wait to use them until you know what you need. Marines should be given hills defense and mountain defense 3 for example if possible (for using as effective pawns with high withdraw chance), and tanks just beg to have CR3. Sam Infantry and Mobile SAM require Interception and Mobile Artillery likes Barrage. Bombers really enjoy evasion and fighters like being promoted in strength.
Once you get flight, you can use it for many things like spreading espionage and corporations/religion via airdrops and if you have a vassal somewhere near an enemy you can also spend 2 or 3 turns landing in an invasion.
You can also abuse this by telling a friendly AI to cancel borders with your enemy - now, your units have somewhere to go heal where your enemy can't get to them without getting into another war.
Your navy is important, but remember destroyers do NOT promote to stealth destroyers. Attack subs and stealth destroyers are hard to deal with. You can also send in transports unprotected because they are so expendable that you can drop off units, delete transports, then produce more. really, it is no inconvenience.
If you anticipate to use the UN for NO NUKES, make sure to set some in your build queues - for some reason this does not stop nukes and ICBM's your actually working on. I don't know about ones set to your deeper queue, but i know for a fact that if it is voted on, and nobody has them built yet, the AI usually says yes, then you get to finish the ones you were working on.
Nukes can be better to use in the field than in cities sometimes because if you can nuke an SOD, you can can promote those useless calvary to also useless gunships and make the kill on their damaged units. you can also use them to "control" the opponent and throw radiation on their uranium/iron/oil etc resources so they cant build improvements. it works especially well when your opponent has no rocketry.
Lastly, you should use spies to crack down on those SDI's, internets and spaceship parts. you can interrupt them and i dont know about SDI but you can "sabatoge project" on things like apollo program. Hatebuild the internet even if you don't need it to deny the AI of it's benefits. Don't be afraid to turn off your research. Also, if you can, turn off your culture - unless you NEED your people to be overly happy. sometimes 20% with theater and radio tower (or eiffel tower and statue of liberty) is enough to run your happiness on 20%. Never let some psycho like Shaka, Monty or Catherine keep the pentagon, if you can't complete it then use spies to deny others. Due to higher build costs, and the higher rate of hammers you can get, spies are a whole new level of cheap ways to stay ahead.
Good luck, modern warfare is not about "rushes" - it is about moving in the right units with the right promotion for the right job, and after a few good modern games, those early era games sure feel both naked and easier.