I think the first I got was the inverted takedown upgrade...it's helpful in the predator challenges and can be used to take down two guys since you can cut the guy down to land on a guy below him. From there, I would go for a combo of the Armor upgrades and the fistfight upgrades. I didn't use the batarangs much in battle so I didn't upgrade those as fast. Once you get the Cryptographer thingie be sure that your next upgrade is the long-range versions since you can use it immediately to get some of the Riddler challenge items.
"I'm counting on you, ultimate sword" - Jaster Rogue
It depends on how skilled at combat you are, experienced players usually skip all the armour upgrades since they can avoid taking any damage once you've adapted. The remote control batarang is very fun, but there aren't any times when it's actually needed for anything (although it automatically bypasses blocks).
Prioritise with the first three upgrades, the combat ones (first the throw, then the instant takedown, then the x5 combo upgrade. the instant takedown is an extremely useful move.
"I think all you gotta do is find that little black kid, and doesn't that start the whole backdoor option?" -WHiTE_LickR
Highest priority for me was Inverted Takedown and Armor upgrades. Inverted Takedown is just great and makes predator sections go by that much quicker. It's an easy dispatch on an enemy, and sets up easy trappings for the other enemies (who will run over to investigate the strung up baddie, then walk away slowly...) Armor upgrades is just more health, which is always welcome.
Next I'd say comes the combo reducer and Throw/Takedown. The combo reducer will make large freeflow battles MUCH more manageable because you'll be able to squeeze off takedowns/throws that much faster. ESSENTIAL if you're going to do the combat challenges.
Then I'd say comes the batarang upgrades. Mainly the Sonic Batarang, combo batarang, and the power upgrades for those. Sonic Batarang is great for setting traps in predator missions, and combo batarang helps with combat, if you wanna improve your game.
Everything else isn't that important, and can wait. The double/triple batarang is fun, but not really needed. Remote control batarang is fun to mess around with, get the trophy, but beyond that not needed. The Explosive gel upgrades are fine if you like to use it a lot (I personally don't) and the Cryptographic amplifier upgrades are 100% unnecessary. They just make getting around those electric doors a little less of a hassle.