Just started my first game of Commander Ironman, and I've gotten to May 11th with 1 death (to a faceless). My troops have mag weapons and predator armor and the Avatar project is at 7 pips with the first black site mission yet to be done.
I think the best beginning strategy is research-wise start with modular weapons, then alien biotech, then resistance communications, and from there just go through the tree avoiding autopsies except the Officer and the Faceless (for the mimic beacon) as you'll get a few autopsies for free anyway and most of them don't offer anything important really.
Building-wise, the first one has to be the Guerilla Tactics School, which will 1) make it so I never have to bring a rookie ever into a mission and 2) gives you Vulture early on while setting you up for Squad Size as soon as you can get it. The second one is the Advanced Warfare Center, after that you need a power relay, then Resistance Comms and Proving Ground. Proving Ground doesn't help you all that much until you get predator armor anyway.
On the Geoscape I basically just focus on countering really bad Dark Events, like Avatar Project +2 or UFO hunt, and I try to pick up Rookies early on, then prioritize Power upgrades, engineers, and scientists. After getting resistance communications, prioritize making new contacts before scanning. You can delay the Black Site for quite some time, since your only real advantage early on is that the Avatar Project doesn't matter yet.
Tactically I prioritize having grenadiers, and I try to bring at least two on every mission, each with 1 flashbang so that everyone on the squad has an explosive they can use. With only 4 I will always bring my highest level people, usually omitting the Sharpshooter or the Specialist depending on the mission type in favor of an extra grenadier. Once I get Squad Size, I always bring a balanced team + an extra grenadier. Sharpshooters are actually amazing early on as long as you're able to put them on high ground. Give them a rifle with a scope, and they're almost guaranteed to kill or severely injure one enemy unit per turn. With a concealed Phantom Ranger scouting ahead for you, snipers can get a guaranteed flanking shot on every single pod before it even knows you're there or has any opportunity to retaliate, then allowing you to best move the rest of your squad into an advantageous, yet secure position. Then your squadmates should use grenades liberally against any particularly tough or well-covered enemies, unless you have everyone in high cover/high ground and can take high percentage shots at all of your foes. When they get promoted, Rangers always get Phantom, Sharpshooters always get Long Watch, Specialists always get Combat Protocol, Grenadiers 50/50 Shredder and Blast Padding.