You asked

How can I feel more competent as a new dad?

New dads have trouble even holding and handling their babies. Your baby will naturally be more comfortable with their mother. While it will take a bit longer for your child to get physically used to you, you should not give up and hand your child over to your partner. In fact, a new dad should take every opportunity he has to get involved with caring for his child. The more interaction there is between you and your child, the more confident you will be as a parent.
Spending significant time with your baby will allow you to learn what the different types of crying mean. Your child has non-verbal ways of communication and you will notice that there is a different kind of crying for a dirty nappy, in comparison to the cry for a bottle. By becoming familiar with your baby's ways of expressing needs and emotions, you will gain more confidence by being able to act accordingly.
Dads may feel that they cannot “do” anything with their babies. There are quite a few simple things you can safely do with your baby. Just holding your child and listening to music or reading aloud is good for bonding. It doesn't matter what you read or say; the sound of your voice will become familiar and comforting.
Do not hand over your child to your wife as soon as you have a bit of difficulty with your baby. If your wife offers to take over, tell her that you have the situation under control. Obviously it is fine to ask her for advice, but do not rely on her to solve all your baby issues without effort on your part.

More questions

Fathers sometimes struggle to bond with babies as the mum is primary care giver.
Some fathers may resent that they cannot particpate in feeding their baby
Striking a balance between homelife and friends will be more challenging now you're a dad
Your sex life is likely to change while your partner is pregnant
Forewarned is forearmed and by reading books about pregnancy and parenting, you can get all the information you need.
As much as children enjoy roughhousing – even at a very young age – you have to be as gentle and careful as possible.
New dads sometimes feel like they've been thrown into the deep end with child care; they lack the confidence to cope with even mildly challenging situations.