We live in CT and if I were to take a job from a company based in NY, I don't know how the taxes would work. I'm pretty sure I'd have to pay tax in both states (correct?) but would our entire income be taxed in NY (we file jointly) or just the NY based income?

I assume that you mean you would be commuting from CT to work in NY. In this case only your NY-based income would be taxed by NY, but at a tax rate that is determined by your total income. CT would tax your entire income, but then give you a credit for taxes paid to NY (though only to the extent that CT would have taxed that income if it had been earned in CT). Bottom line: since NY's tax rate is higher than CT's (6.85% versus 5%), you will end up paying a bit more in taxes by taking the job in NY.