How many caps do I really need?

It entirely depends on how you want to play the game. If you want to buy the various rare armor parts from vendors you'll need lots. If you want to buy the experimental weapons from vendors you'll need lots. If you want to build large sprawling settlements without farming the materials then you'll need to buy them, which needs lots. Some ammos are quite rare out in the wild (plasma cartridges and cryo ammo) so you'll need to buy those, which will cost lots.

You can easily spend 100k caps on a full set of gear and there are several other expensive items in the game also, and that's if you're fine with just one set of gear. If you want to collect all of the sets then this is going to add up pretty quickly.

On the other side of the argument, you can play the game using only loot that you've prised from the cold dead corpses of those who crossed you, scavenging ammo and switching between weapons as you deplete your limited supply of bullets and completely ignoring pleas from settlers in the wastelands as deathclaws decimate their homes - and if you play like this, then you don't really need any, you'll always end up with more caps than you spend.

There are some Legendary armor piece for sale at a traveling merchant costing 10K+ each. Furthermore building the highest tier shops tend to cost a lot of caps (up to 4K, perhaps even more). In general though, you might be better of picking up usefull Junk, instead of weapons and armor.