It is my understanding that a woman wears her engagement ring and wedding band as a set. Sometimes women get them put together into a single ring. Men usually just wear the wedding band.
Thinking about things like everyday wear and ring/stone toughness are things you should look into when purchasing jewelry. Cheap materials will wear quickly and look worn. However, no need to sell the farm for durable and attractive rings.
I think the importance of rings are really up to the couple. For my husband and I, they were of low importance. We wanted to exchange them in our ceremony but we don't wear them daily. If cost is a concern, know that there are plenty of cheap alternatives. This is my engagement ring. He spent less than $500 on it and I love it! Our saving went to a down payment on a house. This is my wedding band (but I don't wear it often... so grain of salt with that one). However, if you want something a little more durable, this probably won't break the bank. And this is my husband's wedding band.
Altogether, including the fact that I have two of each of our band, we spent $510 on rings.
Also if either you or your fiancée have a job that involves heavy machinery or power tools, de-gloving is a real concern with ring wearers so rings might be a no go altogether.