As many others have said, focus on getting your offensive capabilities upgraded.
So, that's armory, barracks, and the mills required to get your troop upgrades (depending on whether you have the Notre Dame). Markets can wait.
Get 4 workers on the armory, and 4 on a barrack, and another 4 on a mill, if that's required.
Barrack upgrades take a long time, and, so, plan to start them early. If you have two of them under upgrade, the time it'll take you to retrain your troops can be quite significant, so, please plan to stagger them accordingly. So, I might suggest keeping four workers on barrack upgrades, one after the other.
Once the armory upgrade is complete, get those freed up workers upgrading the oil refinery. Once they finish the refinery upgrade, get them on building the air strip.
Among the troop upgrades at the armory, prioritize getting the tank upgrade from the heavy cavalry - this provides a huge jump in health and damage of the tanking unit in battle.
Next, get the artillery, if you're not playing as nation with unique archers; else, upgrade your shooters ahead of the artillery. Keep the armory busy at all times. Plan to gather the resources necessary to start the next upgrade, while one is in progress.
At this point, if you haven't got the seventh house, get the market upgrades necessary to get the seventh house (I had purchased the starter pack, so, unsure of the cost in IA).
Next, upgrade the war academy, as it allows you to carry an additional tactic. Once this is done, upgrade betrayal at the armory. Betrayal upgrade from level 1 to 2 provides a huge jump in its effectiveness.
Next, upgrade your alliance gate - there are two levels of upgrades available in IA. You may plan to do this earlier, later, or in parallel to other upgrades, whenever possible.
Next, focus on upgrading the mercenary camp. Unlocking the Flammpanzer tank provides a good boost to your offensive capability in wars.
In terms of upgrading defenses, upgrade one stable right away - this upgrades your forest defenders to tanks - a significant jump in defensive capability.
Next, upgrade your cannon towers to anti-tank guns - this provides the maximum boost to your defensive capability - the jump in the damage caused is quite significant.
Avoid building a bunker till you upgrade at least a few cannon towers to anti-tank guns. It's best to place a bunker (and the likely path the heavy tanks will take) within the range of an anti-tank gun or two, but, in a separate section, separated by walls - if your heavy tank gets betrayed, your anti-tank guns will help in shooting down your betrayed heavy tanks, before they'll cause too much damage to your base.
The library has two levels of upgrades too.
Focus on completing at least till chapter 3 of Savings chapters, so that you'll be able to hold 6,000 oil at your vault.
Next, focus on completing at least till chapter 3 of Aviation chapters (unlocked by the second level of library upgrade, and at least one chapter of the preceding research) - this will allow you to carry two planes, even if you take time to get your air strip upgraded to level 2.
Don't neglect your Negotiations chapters too - if your defensive upgrades are going to lag behind your offensive upgrades, making effective use of peace treaties is crucial to minimize loss of resources. Find two medal ranges - one, where you're able to gather resources effectively, and another, where you can park safely (there are medal ranges where you're prone to repeated attacks by raiders and demolitions, where you'll lose resources to repeated attacks, without getting a peace treaty, and another, where attacks against your base are typically full scale attacks, who flatten your base completely once, and leave you with a peace treaty for a good 12+ hours, protecting you from further loss of resources - when you're logging off for the day, park at the range where the second behavior is predominant - you'll lose lesser resources by doing it).
Anti-aircraft guns can wait too. Build them when you have completed at least one stable and a few anti-tank guns.
I haven't spoken about the factory, because, I'm playing as the French, and I'm yet to build one. If you're playing as the Germans or the Romans, you might want to fit in the factory upgrade somewhere, as getting your factory to level 3 unlocks the heavy tanks for you. In that case, it's important to complete the chapter which adds splash damage to your heavy tanks at the library.
Overall, Industrial Age is a lot of fun, and I'm sure you'll have a good time with playing the game! Feel free to stop by and ask any questions as you progress through IA, and we'll be happy to help you!
Cheers and happy gaming!
