what kind of corp we need for website based business

I am not your attorney and I am responding only for educational purposes. You need to contact a lawyer in your state to discuss this matter.

If you have very little money your options are fundamentally limited.

I guess it's safe to say that you are asking this question and not your European friends because they have found out what it costs to set up an entity in Europe, and that all of you can't put up the statutory capital requirements. Plus, accounting fees to file your returns in the US will be less than in Europe. Yes, you will have to file tax returns and pay taxes in the US, and if you have any income coming in to this entity in Europe, in each of the countries where your 3 friends live. You'll get a credit on your US entity return for the taxes paid in Europe but those taxes will have to be paid.

So, if this decision has been made and it's a US legal entity that you are looking for you'll need to take into consideration where you live and what the applicable tax rate will be. If you are in NYC that's a problem.

The short answers are either (1) a Nevada or NY LLC electing partnership status, (2) a US C corp (NY) if the dividend rate is favorable in the country where the 3 Europeans live.

This assumes you want to be fair to your European friends. If not, there are other US entity and structure possibilities.
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I would strongly suggest that you find a corporate/tax lawyer who can advise you on how to set up this up. You're not going to get a really effective answer here.

Good luck.

You need to determine where you want to incorporate first and then take a look at the various options available. Cheapness is not a good criteria for choosing a serious business format. Since it sounds like this is going to be a transnational venture, you likely will need a law firm that is licensed internationally as well as in the US to advise you.