I don't think there should be a minimum. What I don't understand is men that go beyond their means to buy a ring (on credit) that he can't afford and ends up putting himself and his new wife in debt before they even get married.
It is the intent of the ring that is important and not the ring itself.
Sometimes the ring is a free gift from a family member or tradition. If you are concerned about the cost of the ring I'm afraid your values are not about the sanctity of marriage or the true value of your fianc.
There are some who get married and all they have is their wedding bands. You can't really set a minimum price because the intended groom should only pay what he can afford and never go into debt for an engagement ring. Especially if the debt is so much that he can't pay it off before the wedding. It is never a good idea to start a marriage in debt.
Some women expect a huge diamond which is fine if your man can afford it...sometimes an engagement ring is never given, just the promise of marriage...its pretty much up to the couple...a man usually knows what his girl is expecting...I think starting off small is great and as the years pass the ring can always be upgraded if necessary...I personally put more emphasis on my wedding band...I was given a 11/2 carrot which I cherish and even though an upgrade would not be a problem for us now, I wear my ring proudly everyday.. even if my husband presented me with a ten carrot I would NOT replace the original ring...way to sentimental.