Sorry to disappoint u maybe with this, but u shouldn't use money first on upgrades since they are not changing anything. Buy all classes and if u have spare money to throw around, sure u can use on upgrades.
The damage u deal is exactly the same with +0 and +5, defense and speed and legit everything else what is listed for upgrading (note that game had long ago different way of upgrading but it was game breaking so devs removed it). The only difference is how u progress with time as player and understand game more, how much damage ur character deals and how exactly game works, because this isn't another game where 'X class is better than Y class', it's skill based game. So as example, how u aim will make u a great sniper, not how many upgrades u have.
Hope this explained it.
Also if low money bothers u, there is cash booster which always gives u double cash for 1 month I believe its 2$ only.