Your contacts should be Google contacts, not SIM card contacts. Go to Contacts, Menu, Sim Management and Copy contacts from SIM to your Google account. Then, since there won't be anything on your SIM card but your subscriber identity (that's what SIM means - Subscriber Identity Module" - IOW, "which phone is this?"), it can't run out of space. (If you still have the old phone, do it on the old phone, connect via wifi and sync your contacts (in your Google account in Accounts. Then the new phone will sync all of them and you won't have to enter anything by hand.)
If you want to fix the duplicates, first finish getting the new phone set up. Then delete all the SIM contacts on the old phone (Contacts/Menu/Sim Management/Delete). You're getting a contact on the SIM card, and you're getting the same contact on the Google account. SIM cards shouldn't be used to store contacts on iPhones, Windows phones or Android phones - they all have their own contact storage methods. SIM card contact storage is feature phone technology (15 years old or more), when phones didn't store contacts themselves, and the only way to "sync" your contacts was to save what was on the SIM card to your computer. (I really wish Google would eliminate the SIM card as a place to store contacts - it would save a lot of confusion and problems.)