Now that I'm back on the market again after 5 years and 3 kids,should I stick to single parent guys?

First of all, to start a full life makeover, don't worry about what kind of guy to go after. Right now is the time to focus on who you want to be. Who you are is what will determine your confidence and what you portray will determine who you attract. It's easy to think you know who you are, but you've just spent five years of your life on a path that wasn't right for you. Focus on you, the rest will come.

For male companionship in the meantime, while I don't suggest actively seeking dates, as I said this will come in time, I do suggest men who have kids as you have common ground. That doesn't mean you should turn down a man who has no kids, just that it's easier for a man involved in his children's lives to know what being a parent means. Since your children come before him, it's important he understand this concept.

Not necessarily. Don't limit yourself and just look for someone who will love you, be what you want and need and will like your kids. That's what really matters.