CT W4

If your wage income is mostly or entirely from work done in CT, I would pick the second option, "My expected annual gross income is greater than $15,000".

The wording on the form could be clearer, but I think that the last option is for non-resident employees who work both within and without CT during the year.  Such employees would want CT withholding only on the CT portion of their income.

As a permanent resident of NY, you will file an NY resident tax return that reports and pays income tax on all your world-wide income.  If you physically work in Connecticut as a commuter, you will also owe Connecticut income tax on a non-resident return, but only on your income earned in Connecticut.  That means your wages will be taxed in both states, but other income like investments will only be taxed where you live.  

New York will give you a credit for income tax you pay to Connecticut.  Since the rates of the two states are very close, you shouldn't owe too much extra tax in New York on your wages, but you will be taxed on other income, so you may need to make quarterly estimated payments to New York depending on your other income.

I agree that choice 2 is more appropriate if this is your main job, it sounds like choice 4 would be more appropriate if you had a small side job in CT but most of your income was from elsewhere.