In my area, people usually get gifts at bridal showers. For the wedding, most people put money in a card. It used to be that bridal showers were for dish towels, kitchen utensils, and other inexpensive things. Now people get their sheets, towels, dishes and cookware, small kitchen appliances etc at the bridal showers. Many people use the money from the wedding toward their honeymoon, since they already have everything else they need for the house.
Cat, the wedding as you explain it is what I have heard of years ago. The bride was expected to bring a dowry to the marriage. The bigger the dowry, the richer the husband. If you have a wedding and don't want gifts, you will have to specify "No gifts, please" on the invitation, and most people will bring a gift anyway. It is the way things are done in the US. Maybe you will choose to go back to Romania for your wedding. Either way, I'm sure your wedding will be beautiful.
Different areas do it differently. I once went to a wedding in Nebraska where the gifts were opened during the wedding ceremony and put on display in the social hall of the church. After the ceremony, everyone went to the hall to view the gifts and have cake and coffee. That was the reception. Of course, this was 40 years ago. They might not do that anymore.
I would agree with those who say to get just what you need now....something nice, but not extravagant. You might not be interested in the boys at your college, but when you graduate and go out into the workforce, you will meet many educated, gentlemen who are worthy of you, and you will want to be married.