Everyone has their own style of play and you have to develop one that fits you.
1) If possible, try to save AP points. You will need them in 1942 for a lot of things. Such as building Tank Corps, Art divisions, replacing losses, hopefully a few command changes.
2) I lock on my aircraft to manual upgrades at the start of the game. Then I will unlock a few as the game goes on the pool builds for the upgrade path that I want for the aircraft to save on AP points. If you unlock too many, you will get a yo yo effective - trading up to good aircraft one turn, trading down a few turns later. So it's a little bit of a balancing act.
3) At the start of the game, I set all the HQs to 0 support except STAVAKA which is set to 9. After about three turns, about 90% of the SUs will end up at STAVAKA. You can then do a rail road tour around the front to parcel these out at no AP cost. When you do, LOCK the HQ to prevent migration. Its a pain in the butt, but worth it in the long run.
4) I have a set SU allocation I prefer for each army rather than move the SU around - which can get expensive in terms of AP points (on the other hand, it saves ARM pts). You will get a different opinion from everyone you talk to regarding the right allocation from zero SUs to massive numbers. Pick what works for you and adjust depending on how your doing. My base starts with 2 RKVG art regiments, a MTR battalion, a PVO regiment, and 2 or 3 sapper regiments. I put my RR construction units at the Front level. Note that I start building this up after I allocate all the SU units that have migrated to STAVAKA and been sent to the HQs. So a lot of the art regiments are assigned this way rather than built.
5) You need to change leaders out at the Fronts and Armies. There are several post that are stickies that talk about this better than I can. This actually uses up a lot of AP points early on but you have to get good leaders in position.
6) Regarding tank bgs. I don't build them. You will end up with over 100 in early 1942 which is more than I can effectively use. I plan to convert these to Tank Corps and usually end up with 20 to 30 tank corps depending on how badly the German is beating on me. Any tank bg above what's needed to eventually convert is just wasted IMO as its a rather minor combat unit and takes a lot of trucks to supply.
You will get different opinions on this from people - and I don't put myself out as "one of the best". So read a few AAR and some other post and make up your own mind.
7) Cav divisions. I may build a few depending on how I feel and how many I have lost. These are you best units for the first blizzard when combined in a corps but they are expensive. Frankly, its more of an emotional decision with me and usually made on whim. Not the best gaming decision. But then again, I the group I play with plays more for the enjoyment than for the blood.
8) If you just have to burn APs or lose them, the gentleman who pointed out building inf bgs is right - even though you will get nearly 100 of these in 42, you can combine them into a division or corps later. Ideally, you should target an army of 150 or so infantry corps. They are several ways of getting there. And inf bgs are on all the paths.
9) In December (I think), you can combine three cav divisions into a cav corps. Create as many of these as possible. You can put four of these corps in an army without overloading it. Most of the people here recommending keeping your Shock Armies for that. You really shouldn't have a problem filling out the 4 Shock Armies with Cav Corps. Attack the Germans where you can win. In most games, I have converted all my Cav Corps to GD status by the end of the first winter. Makes them a lot more useful the rest of the game. If you have extra cav divisions, combine the rest into Corps. If you have a few left over, assign them to the shock armies to get them up to 18 command points. If you have more than that, your doing better I usually do and do whatever you want.
There is a sticky on the Russian first turn - I would recommend that you read it. A little dated due to the patch upgrades but it gives some good advice and got me started.