As an FYI, in some (many?) parts of the US (world?), a big and not-detectable -- without testing -- problem is arsenic in the water. I've been researching this as we've recently bought land with a well (like yours, it is also icky and iron-y). It's naturally occurring and flavorless.
If you're already steering clear of the water where you live now, no worries -- but down the road if you stay on well water and find nicer stuff, probably worth getting tested (at least where I live, arsenic testing in not required for existing wells, whereas other sorts of testing is when they change hands).
Generally, the levels are low enough that there's no immediate threat (no problem drinking if you're on vacation at a place with a well), but decent evidence that even VERY low levels of arsenic are bad for you if consumed over a long period of time.
We just take (good) city tap water out to our well-equipped (ha!) property, for now. If we later decide to build/live out there we'll likely pay for a filtration system.