As the Eastern Entente should I try to press into Hungary with Serbia and Galacia with Russia, and at the same time into East Prussia, or should I pull back my forces in Poland and try and find a defensible position so as to better defend against the advance of the German and Austrian armies?
I assume, we say about the historical warplans here? If so, than, in my opinion, it's better for the EE to defend against Germans and to press like a hell against Austro-Hungary. The 1st and 2nd Russian armies are just not powerful enough to crush the German 8th Army and conquer the East Prussia (geography+strong defenses+railroad net in EP are all against Russians). But the Russian Armies on the southwest front are strong enough to defeat the AH armies in Galicia before Germans could lend them any significant support. The main goal for Russia here is to inflict as much losses as possible to the AH and move to Carpathians. The main goal to Serbia is to tie up maximum AH forces.
In fact - unless you are in PBEM against a strong CP opponent, advise is- Move the second army also by RAIL to support the attack on the KRAKOW-PREZYSML-LEMBERG-CZERNOWITZ line. you will have 5 strong armies against 3 medium armies and maybe a fourth Austrian Army. Odds you can take in early period. Use the 9th Army in Warsaw as a screen in Poland and 1st Army as a Screen in Baltics. In Caucasus also only defend.
Try to crush Austria hard in 1914, as Serbia dogged defense in the mountains and Belgrade is the key.
The Berlin plan is probably the best in terms of activated areas, but I'd be prepared to abandon the Polish salient west of Warsaw if the CP player attempts to cut it off in a massive pincers movement. Austria is the weak link, as others have suggested - it's relatively easy to outflank advances on the Galician front, and if they throw their whole weight against Russia, the Serbians can even go on the offensive. Against a human opponent, I'd play my cards close to my chest against Germany, bearing in mind that that nasty Hoffman decision can be played against any Russian army on German soil, but try to keep a large reserve on hand to unhinge any German advance from East Prussia, should the opportunity present itself.
"I'm ashamed of you, dodging that way. They couldn't hit an elephant at this distance."