I'm not much further along the curve than you: a veteran AT player, I purchased ATG about 3 weeks ago, and am only now beginning to feel comfortable via the AI.
A few points which have been important to me:
1. I've had a much better go playing against multiple AIs, as they tend to duke it out between themselves. Playing one-on-one against the AI has tended to be a stompfest (against me). With multiple opponents, the AI balances its focus between several players, allowing me a bit of breathing room;
2. I tend to send my production directly to my front hq(s), with the exception of the Capitol (as with Josh above) which produces supply/pp/ore as needed directly to 'Supreme HQ'. Previously, I had sent all production to 'Supreme HQ' and divided out as strategic capacity/rail access allowed, but this left my units weak and vulnerable. Also, if you have a few trucks in your front hq, inf can be shipped to its units (w/o trucks they could also 'walk' if within range);
3. I've found that producing Flak right away helps via AI air strikes. My initial production is to dump 40 staff and 4 Flak into an empty hq. While I don't know the mechanics of AI air strike determination/combat, I've had the distinct impression that units within range of the Flak sustain far less damage, and the Flak seems to deter attacks altogether sometimes. On a related note, keeping units in rough terrain (e.g. forests), especially if they can entrench, goes a long way against the AI air strikes;
4. Noticing MGs defend far better than attacking (and I always seem to lose a lot of them when attacking), I've gotten in the habit of putting all of a group's MGs in one 'strong point' defensive unit (currently 40 Rifle, 10 MG), which I don't attack with but use to defend key terrain or use as cover while a weak unit reconstitutes. This has been working well for me.
5. Regarding ore consumption, as a matter of preference I sequence my production prior to using my engineers for anything, and be sure not to use more ore than I need for production. I like to go on an ore binge with my city production if I know I'm going to need a lot of ore the next turn. Also, are you using your engineers to upgrade your 'raw' sites to level 2 production? This makes a big difference.
So none of the above I'd claim as a hard-n-fast rule, but they are some things which have helped me as my play has evolved. I hope this helps. Cheers!