Part of my job is identifying and controlling fraud in addition to being an accounting expert witness after the fact so I try to stay current on fraud prevention techniques.
Last year I went to see Frank Agagnale (think "catch me if you can" movie) speak at a banking function and frankly it is so easy to access data these days that people who are going to commit fraud can do it in minutes. Your fraud could have been perpetrated by anyone and if they get the last four digits of your social you could have a lot of issues. I would strongly (as did Frank) that you get a credit monitoring service, but the key is that you make sure that they check your data as soon as an application is made. Also once they have your information another scam is to change one number or letter in your name and set up an account that won't be caught for several months and in that time they will charge up thousands, when the mistake is caught they will associate it to you because they will assume it is a minor transposition error, then it is on you to prove that you did not cause the charges. If you want to pm me, I will tell you who I use or check his website.
Biggest thing is to use credit cards to pay for as much as you can and monitor your charges regularly. You are using their money to pay for things. If someone scams your debit card, that is your money and you will never get it back. Just because you are safe now, doesn't mean your information isn't comprimised, they will sit on it for six months to two years before using it in a lot of situations.