Ground Attack, Support or both?

Ground attack (and ground support for that matter) on dug in units is usually a waste of time and effort. If you want to speed up breakthroughs then ground support seems more appropriate as it will help reducing org a little faster so you can dislodge the defending units.

Ground attack reduces strength points and is useful on fleeing enemies. When you have encircled several units you can use logistical and/or strategic bombings to reduce the infra level so they cannot recover org that quickly (if at all).

Ground support!!!! I use it like crazy. Fighters are decent against small groups of units and bombers, especially TACs, can handle larger stacks. I think it helps more with exploiting the breakthrough than anything else. If you 'walk' you air support ahead of the spearhead it will only take a day or 2 to knock out any small straggling groups of 1 or 2 units. If you

For Barbarossa, ground support (although in WiF2 most of your airforce IC should be in FTR or INT on Air Superiority...) The reason support over attack is that you can't really chew through Russia's IC on reinforcements like you can against China as Japan; and your goal is to encircle units, not wear them down via a campaign of attrition. Thus, you want low org units that retreat quickly and can't mount effective counter-attacks against your spearheads. Even better might be to use about half your TAC on logistical strikes on the provinces you DON'T plan to attack through; to slow the Russian movement speed and weaken their counter attacks (ESE). It allows you to hold a pocket with less troops and/or gives you more time with a mobile defense plan for reinforcements to arrive at the breakthrough and launch-off provinces, and on the back of the pocket slows the retreating troops to give you more time to close the pocket. If you do use Log strikes its important to have the correct doctrines for bonuses or it doesn't work nearly so well.

Usually I use the hotkeys to micro my TAC and CAS stacks (ctrl-1,2,3...; 1,2,3...) and target provinces individually for logistic strikes, and by area/region for ground support as the bomber AI will prioritize active combat over inactive provinces.

edit: In general; both Ground Support and Ground Attack are useless against provinces that are not under attack by ground forces. During active combat ground support is most effective, i.e. will help you win battles more. After the battle is won, Ground Attack generally is best (a lot more damage to a unit's combat strength, while allowing them to regain ORG; vs continuous support doing little strength damage while keeping org at a low value.) However in the specific case of Barbarossa continuous support makes more sense (plus you'll probably have multiple provinces needing support, so little time to get in ground attacks.)

Ground support where ever you are going to attack.
Ground attack should be used mostly on retreating units as they are not dug in and they cannot reinforce while retreating.

I use them the same way as described above. The only time I use Ground Attack is against retreating Mot or Arm, because this attack is very effective and that it takes longer and is more costly for these units to be repaired. I usually don't bother with INF since I want to keep my air force with the highest level if Org.