The first thing you need to realize is you are not alone in the battle. It will take all 3 Allies to beat the Axis, but due to other priorities you can't really expect significant help from the UK and US until round 4 or 5 (outside of some air support). So, what is a good way to set up a solid base and ensure your survival until the Allies can take some pressure off of Moscow?
Lets take this step by step and start off with your purchases.
Russia has quite a few options, but I'm only going to list 3 basic buys (with one alt) which most others can then be adjusted from.
The conservative play (8 inf buy). 8 units, 8-attack, 16-defense
This is great for defensive purposes but due to Russia's placing limitations, it restricts what Russia can do in rds 2 and 3, in terms of detering German advances, and might leave you a little too weak offensively. You also lack mobility since you only start with 4 armor and 2 ftrs.
I do not like this buy, b/c an aggressive Germany player can take advantage of the lack of early Russian firepower and mobility. Just a bit too conservative for me.
The middle of the road play (5 inf, 1 rt, 1 arm). 7 units, 11-attack, 15-defense
You get a little more punch with this buy and it only costs you one less unit and one less defensive point. You can place 3 inf, 1 rt in Cauc and with the rest in Moscow and you now have potentially 5 armor to use on Russia 2.
I certainly favor this buy over the 8 inf purchase, and is good for beginners who want to attack or at least threaten multiple territories while still providing a solid defensive base. This buy will not lose you any games.
The aggressive play (3 inf, 3 arm). 6 units, 12-attack, 15-defense.
I term this aggressive b/c you are only buying 6 units, you do add 12 attack points and still get 15 for defense, but you don't have quite as big of a stack of infantry as some players may like.
I really like this buy and teamed up with an infantry retreat (Eve, Novo, Kaz) you can really put a serious threat on Germany's eastern borders (Ukr in particular) and force Germany into thinking twice before making any aggressive moves into the East. Also you almost match Germany interms of armor since you should have 7 on the board and right on the front lines.
(Note: an alternative aggressive buy would be the 2 inf, 2 rt, 2 arm buy. 6 units, 12-attack, 14-defense <– I like this one as well.)
Now to your Combat Moves.
In my opinion Russia should be very careful in not overextending themselves and risk too many losses on R1. I think there are some solid "basic" attacks that Russia can do to inflict enough damage on Germany or stregthen your position. I would limit my attacks to 1 or 2 of the following 3: Wrus, Belo, and Ukr. I think Wrus is the only must attack and your other attack may depend on a possible bid placement.
My early preference has been to attack Wrus and Ukr with max available Russian units (assuming no bid units to Ukr). However, lately I've been just attacking Wrus with about 10 inf, 2 rt, 2 arm, 2 ftrs. I like the idea of trying to limit Russia's round 1 losses and with an "aggresive" buy, Germany will not be able to stack Ukr on G1 and you can just trade Ukr from R2 on.
You leave an extra German ftr, but I think it is essentially a wash between killing the fighter and losing 1 rt and 3 arm. As long as you went with an "aggressive" buy you should feel no ill effects of leaving Ukr as is, but I'm certainly not going to fault players that want to take out that fighter.
In terms of the Belo and Wrus Attacks, I prefer to just attack Wrus in that case, again to minimize Russian losses and IMO Belo is not a priority which means the Germany player doesn not have to counter it on G1 which could mean a heavy Germany move to Ukr early esp if you took a few extra losses in Wrus as a result.
Now that Combat is done, you'll want to land your fighters in Cauc and non-combat any available tanks there and move your Moscow aa-gun to Wrus and your sub to sz 2. I prefer to retreat all my Eastern infantry one territiory to maximize the early pressure on Germany as well as cutting down my supply lines while increasing Japan's. It really does not hurt you to give up Bury, Sfe, and even Yak in the first 1-3 rds. Together they are only worth 3 ipc and if you can get and hold Ukr b/c of it it is well worth it. And if Japan gets overly aggressive it isn't too hard to pickoff 1-2 inf with the Allied forces already in Asia.
Now it is time for placement, you want to place 4 units in Cauc with the rest in Moscow. Always place armor in Moscow, since they can move 2 spaces, until you can take and hold Ukr.
A typical summary for me, if I go 3 inf, 3 arm with only the Wrus attack will look someing like this:
Wrus: ~8-9 inf, 2 rt, 2 arm, aa
Cauc: ~6 inf, 3 arm, 2 ftrs, aa
Mos: 4 inf, 2 arm
Yak: 4 inf (or 6 inf)
Novo: 2 inf (or 0 inf)
Kar: 1 inf
Sz 2: 1 sub (with UK ships)
This isn't the most aggressive opening but I find it to be very solid and very tough to crack, and you haven't done anything that gives Germany/Japan a big opening or willl cost you the game. You've got a mobile army, where you can add 1 tank per turn, and a strong power base in Wrus, Cauc, and Mos. This also allows the UK and US some freedom to do different things since Russia does have a strong central location and isn't in need of immediate air support or reinforcements.
This opening also will work with most if not all bid placements of 8 or under.