Hello Rodimus,
I'm more than double the age group you are asking information from, but maybe I might be able to help some FROM MEMORY.
What kind of sermon appeals to you? (ex. object lesson, story)
At that time in my life, my wife and I were raising two children and working several jobs to pay the bills. We went to regular services, but special and additional services might have been helpful in life skills (i.e. Christ the Head of the home, raising children in the Lord, being a good steward of money and other blessings from God, and other issues for young parents trying to raise children).
What kind of worship appeals to you? (ex. contemporary, mixed)
At this time in my life, this service would be extra and in addition to services we were already attending. So, I really don't know that another very formal service would serve as well.
What kind of atmosphere? (relaxed, busy, comfortable)
Again, this would be an extra service in addition to normal services. I would think that a more relaxed style would cause more young parents to come, especially if it was also a social time to enjoy the company of other Christians in their same age group. This would be the end of the week, and the young parents would probably be tired from a week of work, so something more relaxed might convince more to come. I could visualize some coffee, soft-drinks, and maybe some finger food so that some could skip dinner and come to the service instead. Let's say that the subject was raising children in the LORD. I could see the teacher or instructor as a facilitator and discussion among the parents attending. It could be a time of sharing the word, talking specifically about Biblical principles in parenting, and group involvement with problems they were currently experiencing with their children. I think that services of this type would serve many purposes: 1) encourage friendships between young parents that leads to Godly fellowship; 2) help young parents with a difficult time in their lives while they are struggling to be Godly parents; 3) the children of these parents would hopefully benefit the most by having Godly parents who have been strengthened in the Lord.
This is just an idea from an OLD GUY.
I hope that I helped some.
Love In Christ,
Tom
Psalms 103:17 NASB But the lovingkindness of the LORD is from everlasting to everlasting on those who fear Him, And His righteousness to children's children,