I'm glad you are considering your children's needs, S.. It is unwise to start dating again before you're divorced, or for a good long time afterward, until you have established a steady and predictable life for your little ones. Please, please please, wait and focus on being a mom. That's your job now.
And please consider getting counseling so you'll make better choices about future men in your life. I say this not because I know you or assume you can't be smart, but because that's how we are constructed emotionally. All of us, until we find out what our own patterns are, what our real, authentic needs are, and how to look at our lives with more objectivity. I had to do this when I left my first marriage, and it was the healthiest emotional investment I could have made for myself or my daughter. And it relieved me of a "need" to "be completed by a man," and gave me time to establish a good long emotional distance from my ex.
As far as introducing men to your children, don't. Not until you are pretty certain you will want to marry someone. The results of rushing that can be devastating to kids, who may love, hate, or be abused by boyfriends.
My mom brought an "almost-daddy" into my life when I was eight. He abruptly disappeared when my mom got pregnant. Turns out he already had a wife and family, and his relationship with my mom was a big lie. I still carry deep emotional scars from that great grief, more than 50 years later. Don't risk doing that to the babies you've given life to.