I like condoms. They are the most effective barrier method. Except for one or two types we've tried, they always feel fine to me, and they make things less messy.
That said, I definitely...um...fifth? the recommendation to look into the Fertility Awareness Method. FAM can be combined with condoms - you can use them only during the fertile phase. Or, if you are really completely paranoid, you can use condoms during the infertile phase and abstain during the fertile phase.
Whatever you want! FAM is really flexible like that. I love FAM even more than I love condoms.
I don't think it would be necessary to pull out while using condoms. Especially since you say having a baby wouldn't be the end of the world. It seems like it would almost increase the possibility for failure, due to the condom possibly slipping or falling off. I don't know.
I do know several people who have condom babies, so it's not 100%, but nothing is. Good luck!