First, it depends on your traits. If you have infantry general, lotz of pioneers is no problem. If you have anti air vet. - one flak will solve your air attack problem.
I play without pos traits and heroes:
1. no bombers at all. Moscow has strong air defence, so Bombers arent effective. Besides, weather is bad often, so you have too many rounds where they do nothing for you. You need lotz of pioneers, they cost you many slots.
2. One 21 cm anti arty arty is needed to be safe of enemy arty.
3. If its too hard, go barbarossa mid, then you have gustav. It safes you muuuuch time and the russian guards wont like it too.

(time is my only enemy on that map, espec. if you want the bonus goals)
4. If you have no prestige, disband a bad hero. I play without heros because of that, its too easy.
5. In the northwest i put ONE greandier inf. ONLY.. Wait for the t34, till he caps your city, then you can kill him easily and you get some prestige for retaking the city. You can use the grenadier to kill the pac, then transform this grenadier into an parachute inf. (city with supply hex) Its only duty: to capture the city in the north, which is only defended by one pac. (this saves you lots of time, otherwise your main pioneer group has to take that city which is often impossible, because it has to repell the russian counteroffensive. Before you do this, you have to be SURE (recon plane), that there are no enemy tanks or infantry near, or your parachute inf. will die fast. (i do it in the end when the enemy counteroffensive is already destr. or at least severly weakend) And of course you need total air dominance when your air transport flies to the city.
6. To take tula i use: 1 pioneer, one good pac (if you are barb. south you should take sturer emil or how the name was) and one stug 3 arty. (it costs only 2 slots WITH one overstrength and shielded by pac it survives tank attacks which can be important when the counter off. starts. Rest as many pz3 as possible. (pziv is anti inf. at that time, dont use them, btw. i dont use flame tanks, they die to easy if the enemy flanks you-pioneers are the go to guys in urban warfare
7.South west i have most of my units: As many pioneers and 150 cm arty as possible AND the 21cm Arty as mentioned before. No flak, its expensive and it doesnt prevent bleeding you dry bec. of bombing. I use 3 Fighters and i DONT attack with them. Place them BETWEEN your artys, especially the 21cm arty is a magnet for russian bombers. So you dont have to hunt them, they bomb your arty and get severly damaged by your fighters, in ai round. And in your round you finish em completly. (but dont let your artys unguarded, when you finish the planes or bleeding starts next round...) That way you loose much less prestige and the russians loose their air force fast. If you dont have enough slots, maybe one fighter-bomber is a good choice. 2 slotz only WITH one overstrenght and you can finish weakend russian air force with it. Use 1 or two scoutplanes as shields, over prototypes. AI loves to bomb emil gustav etc..
8.A good formation of elite pioneers has no problem cleaning the city from southwest to north, north east. With green pioneers you will have a hard time against the russian guards, even WITH arty support. Time is a problem in that case. Prestige less, because of cheap reinforcements.
9.The tula group pushes north east and takes the vic there. NEVER leave your tanks without protection of emil or you will suffer. (if you have std. pac only use an overstrenght pac, its imp. that your pac punishes the t34s and kvs, bec. your pz3 are no match. German tanks are simply not competitive, at that time.
Good luck