The Hysterical Koala
others are far more qualified to give you advice than I am, but here is a start. (I don't have time to go through the entire game, but picking is important so let's start with some more basic advice)
Each player is given 3 spots initially, as there are 2 players you only need to have 6 picks.
Don't pick in bonuses with wastelands (them giant neutrals that are so annoying to kill!). Look how long it took your opponent to take a bonus! picking is primarily about 3 things:
Efficiency of bonus + how fast can you capture it? In this kind of setting, you MUST have at least one bonus by the second turn, in almost every case. Eliminating an opponent's spot usually can't compensate for a drastic deficit in income, that usually proves fatal in the end.
Long term expansion (is this the only bonus you can feasibly take in the area?) Try to pick +3 or +4 bonuses in the middle of clumps of bonuses that you can quickly capture. Being able to capture several bonuses within 2-3 turns of each-other in a single area would be quite nice.
Map Coverage - clumping all your picks is quite risky. IF you can reach all the major areas of expansion easily, it is easier to outgrow your opponent.
There is a fourth factor as well - the First Turn Bonus (FTB). Thsi sometimes comes up, a bonus you can complete immediately, with your starting deployments+income. You generally need a plan to either counter this longer term, or right away (with a counterpick, or deliberately taking a spot in the pick chain, but not necessarily the first one.) Less experienced players generally should avoid FTBs in competitive matches, since the lack of map coverage, and the opponent's likely intel on your position will allow a smart opponent to try and box you in, preventing you from growing far beyond your initial bonuses. With a fTB you have to be able to annihilate your opponent quickly, the longer the game goes, the harder it is to maintain an advantage.
Looking at your specific game, the areas of expansion that come to mind are:
Africa: (very minor)
Antartica+South America+Australia (minor but potentially useful)
West+East USA (Minor, slow to capture but doable. safer income because of only one viable pick in the area)
And of course, the big sprawling behemoth also known as Eurasia - spanning from Greenland all the way to China, with no wastelands for relief from the action anywhere to be found! (Russia is on the edge and doesn't count) :p
It's important to note that Eurasia sort of connects to the U.S. and the SA+Antartica+Australia combo, but not directly, and only through chokepoints. Africa is also reachable, but only through bad bonuses. East Africa and Antartica also reach eachother through a single chokepoint.
Keeping this in mind, I probably would have picked something like 1. Antartica, 2. East U.S., 3: West Russia, 4, Central Russia, 5. East Africa, and 6. Southeast Asia.
The idea here is to try for better bonus defensibility, with two of my picks (Antartica, US) and to lock in safe expansion. With my other picks, I would aim to either disrupt the potential FTB that is Central Russia, or to jointly 1. outexpand my initial picks, and 2. Use the intel I have on my opponents position to send stacks into the safer territories, by going into the choke points first. If I have an opponent in my "safe spot", for instance, I get Antartica, and the opponent gets South America, then I can 1. complete my bonus faster, and 2. I can outexpand my opponent in the local area, since I can reach Australia and Africa even, while he has to travel a long way, or break through some nasty wastelands to grow from there - neither of these are a good option since we would meet quickly on our borders and start fighting, or at least deploying to block the opponent.
BTW there is also some subtelty to the picking order and possible combinations, but others here can explain it FAR better than I can!
Edited 1/9/2016 15:13:20