Demigod is a game of complex interactions between the mechanics and thus complex benefits and costs to your actions. Every choice, in this case upgrades, has to consider more than just "will my DG be more powerful quickly enough if at all". Even the choice to upgrade gold is not a matter of sacrificing the time it takes for your team to recoup the cost of the upgrade in gold earnings. A less item dependent hero (e.g. idols/support Sedna) purchasing this will provide a good boon to the assassins on your team who need strong items to be effective without setting you back too much.
Let me give a more detailed example. I dont think anyone has mentioned flag capping yet. Upgrading creeps is a foolproof strategy to improve your control of the central flags which will, in turn, be worth many times the cost of the upgrades. Try playing the map "Brothers" without upgrading you creeps against a team that does. You will lose. That 1800g you got some extra mana or health with instead of priests just handed your opponents the artifact hut, nuetral creep portal, and celerirty flag. They will use that portal to push down your outlying towers, teleport to their flags for instant front line support, and will continue to upgrade using the extra money they are earning. You will be confined to your base which will become increasingly difficult to defend. You might be able to counter this by turtling and building a late game regulus or rook, but you will probably need a bunch of defensive citadel upgrades to do it. ...or you could just buy priests (and the others later). One person spends a little on extra creeps or the entire team has to be able to hold flags against harder enemies and one person keeps a little gold.
To cover all cases and provide a prisoners delima type arguement: Assuming teams are of otherwise equivalent skill you have the following options: either upgrade creeps or not, they can either upgrade creeps or not.
1) You upgrade creeps and they upgrade creeps - equal footing.
2) You upgrade and they dont - you have the above advantage (assuming your team can capitalize which is relatively easy).
3) If you dont upgrade and they dont - equal footing.
4) You dont, they do - disadvantage as described.
Hence you should always upgrade because the worst case is even chances and the best is an advantage. The only real skill involved is choosing who will pay for the upgrade.
This kind of analyses can be applied to most of the upgrades with different results. I believe the creep upgrades (HP, DMG, priest->giants) are the most universally helpful ones as you will eventually always need to push to win (except in DG kill limit mode). Some others become rather worthless depending on your strategy. (e.g. why would you buy tower damage if you bought priests and creep damage to keep the lines pushed).
If you really dont want to think it through, here is a guide:
*Always buy: Priests, lvl 1 creep damage
If you are getting outpushed, buy: Angels/Cats/Giants, lvl 2 Creep damage, Creep health
If your support character has early extra cash, buy: DG XP boosts, extra gold
If you are playing "forts"mode, buy: Building HP/regen
*Never buy: Death penalty, tower damage
Comments?