If you're on F1 status then your days of presence are exempt from counting towards substantial presence test. Obviously you're neither a citizen nor a permanent resident in the US. As such - you're not a US resident for tax purposes.
The correct form would be 1040NR. If you're qualified, you can use its simpler version - form 1040NR-EZ.
You should not be filing form 1040, or any of its easier variants (1040A/1040EZ) since it is for tax residents which you're not. You're expected to report worldwide income when filing the form 1040, and pay taxes on it.
If you used some cheap tax preparation outlet, they are usually clueless about taxes and can only put numbers in the fields on the screen, so they'll file for you the only thing they know. But that would probably not be the right thing for you.
Filing a wrong tax form will not necessarily cause troubles when applying for green card, but it may trigger an audit later since you may inadvertently claim benefits you're not entitled to. For example, you may have claimed a standard deduction, but unless your country has an explicit provision in a tax treaty to allow that - you shouldn't have.
To correct the incorrect filing you should fill the form 1040NR/1040NR-EZ, attach to it the form 1040X with the explanation of what it is that you're fixing, and file with the IRS per instructions.
If you paid money to that preparation firm - you should go back there and demand that they do that (filing the correct form and the 1040X) at no cost to you since they should have done it right to begin with.
If you fill the form 1040NR and end up with the same tax liability - you may just leave it as is. As long as everything was reported correctly and all the taxes paid - you didn't break any law by just using the wrong form.
However, if you plan filing as non-resident next year or claim treaty benefits/exemptions - you better fix it.