MAA (only have experience with MAA on iOS) the game goes through "seasons". A week or two where nothing special is going on, then a PvP Season will start. Before the PvP Season finishes, a Spec Ops will start. Then the PvP Season finishes. Then the Spec Ops finishes. Then there is another brief respite from the frenetic activity.
Due to the way the different activities start and overlap, I've found that this is a specific time for farming for specific resources. Granted, this is my opinion and based heavily on my personal MAA game play philosophy. Presumably, everyone wants as much of everything as possible, so I think my thinking should hold true.
Special Ops Heros is a special category of farming. Due to the fact that Special Ops Heroes will be eventually released for 200 Command Points (equivalent to 100 Gold), it only makes sense to make every attempt to complete all tasks to obtain the unlockable hero -- skipping the last task (for 25 Gold) as necessary. Because this can only be done during Spec Ops, it seems this should be a clear priority "farming" activity during the Spec Ops season.
Lockboxes are obtained from Spec Ops Deploys, rewards for some Spec Ops Tasks, defeating Group Bosses, and Spec Ops Boss and Epic Boss Roulettes. Right now iOS does not include lockboxes as one of the PvP roulette spin rewards, therefore, Spec Ops are currently the only time to obtain these. This should make lockbox farming the next highest priority during Spec Ops. Because the reward for opening lockboxes is random, it's not econmical to purchase lockboxes with gold, and only makes sense if you just can't live without having a particular lockbox collection hero. I presume that eventually the PvP spins will give lockboxes, and I can live with waiting to recruit the lockbox collection hero at some later date.
Gold is fundamentally "farmed" by leveling up your hero, 4-Starring missions, as rewards from the Daily or the PvP Roulette, or by performing the TapJoy tasks. Therefore, it behooves every player to participate in PvP to win 5 fights a day during PvP Seasons, and playing MAA every day at least around the time of the Daily Roulette. 4-Starring missions could be done anytime, but secondary to completeing Spec Ops tasks for the Spec Ops unlockable hero. It's never a good idea to trade Gold for some other currency or points because Gold is needed to bypass tasks in Spec Ops that can't be completed or purchasing Limited Edition gear. It's rare, and if you don't have enough when you need it, your only choice would then be to buy it for real money.
Command Points are obtained from Boss, Epic Boss, Daily and PvP Roulettes and 5-Starring missions. Again, this means playing everyday at least around the time of your Daily Roulette spin and participating in PvP for a chance at the daily PvP Roulette. Command Points are the currency to recruit heros, and anytime is a good time to farm Command Points. This is basically done by 5-Starring every mission that you're not trying to farm (for Premium or Epic Boss gear) and running Epic Boss missions. I get the feeling that a lot of people are not bothering to 5-Star Spec Ops missions. I think that's a mistake. Once you've 5-Starred all the Story missions, that's it. No more Command Points from those missions except from Boss/Epic Boss spins. It makes sense to try to 5-Star as many Spec Ops missions as possible.
Shield Points are obtained from Gifts and Rewards. You get up to 50 from gifts and another 15 from rewards if you have more than about 35 allies. However, because of the above rationale why Spec Ops are important, Spec Ops is not a good time to try to farm Shield Points. Shield points can always come around later, but when a Spec Ops ends, much of the rewards from the Spec Ops becomes unobtainable (or at least for a high price later). I only focus on levelling heros and getting the Shield Points needed when there is no Spec Ops running. Also, for levels 2-10 of a hero's leveling, Shield Points will be the main limiting factor, but from level 10-12, you will find that you spend Silver at a much faster rate than you can farm Shield Points.
Silver is rewarded for just about everything, but the most reliable source of Silver is Remote Deploys. Even if you haven't upgraded all your jets, you should have as many jets as possible and send your highest level heroes on Remote Deploys as often as possible. When you start leveling your heros above level 10, you will burn through your Silver at an incredible rate. Therefore, because Spec Ops is not a good time to farm Shield Points, it's an ideal time to farm Silver. Take the time during Spec Ops to send your heros off to Remote Deploys and replenish your supply of Silver.