L.B.
Dating is fine if you are ready for it. If you want to explore new relationships and spend time with a woman, then do so. Your children do not need to be involved in your dating life - in fact, it is better if they are not.
My mother passed away when I was 13. After a few years my father did start dating. Honestly, we never met the women he dated. The one we finally did meet - after he had talked, and talked and talked about her :) - became his wife when I was a Senior in High School.
So, date if you are ready. Your children do not really even need to know that you are dating - and if they do, explain it casually. Do not introduce every woman you date to them. Do not bring women home.
Take it slowly.
And I second Wild Woman - do not date solely to find your children a new mom. You would be doing a disservice to her and to your children. Date to make yourself happy. Happy parents are good parents.