Save the PDA until your children know your new boyfriend and are comfortable around him. Once your kids are comfortable hugging your new man or holding his hand, you can be, too.
Don't be the Dad
Make sure your man doesn't play into the "father" role when meeting your kids the first couple of times. That means no discipline and no overt signs of affection. Pressuring them to see your new boyfriend as a father is only going to backfire, bringing up feelings of loyalty to their father.
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Give your children time to get to know your man before letting them see him as a father-type figure. Over time, they will adjust to your guy's presence and this will fall into place.
Focus on Small Doses
Don't overwhelm your children. Let them meet your boyfriend in small, short doses - not for full days at a time. Give them time to process this new person in their lives and form their own opinions and ideas about the relationship. This will allow them time to ask you questions and discuss any concerns with you.
This also ensures your kids don't feel left out or neglected by all the time you're spending with your new man.