Uf, in upgrade games like these, the math behind the different upgrades should be done to prevent huge gaps in cost effectiveness.
In this game, you should buy the guns but not upgrade any of them (none of the damage output upgrades are cost effective). The sole exception is your partner's grenade launcher, in which case putting a point or two into the number of rounds per magazine is very cost effective (100% for $400, then 50% for $440 [or therabouts, forgot the actual price])
You should buy all of the specials (once you have tier 2 guns), but not upgrade any of them either. Surprisingly, upgrading them doesn't seem to make the cooldowns significantly faster, if at all. Use them as soon as they come online so you get maximum uses out of a wave.
In the defenses tab, both the howitzer and the mines should be purchased. The mines are the only other cost effective upgrade in the game, since for base price of $1000 plus $100 per level you get an additional mine, each capable of a huge damage output. Remember to allow enemies to run over them so you get your money's worth. The howitzer is generally useless, but can save your ass in rare situations where the map is flooded with enemies and you can't shoot through the grunts to the explosive donkeys (the howitzer will shoot past the grunts to the explosives and generally clear the map for you).
Other than that, the upgrades are poorly priced for what they do and should be avoided. Fun game though, and interesting concept.