My ex paid nothing before or afterwards until i really put the pressure on him and threatened court and he now pays a measly amount of less than half what CSA would calculate he should. His mother on the other hand was fab, sent me a a big box of baby clothes, blankets, toys and then another one after baby was born. She lives abroad. She has continued to send things and money for bigger things for me to.
Having spoken to other single mums it seems that every day expenses such as nappies aren't things absent dads tend to want to put money towards. But big things like a pushchair they are more ready to fork out for.
Ask him if he intends to help you out with any of the things and if he'd rather give you some money to put towards things or if he wants to get somethign specific. You need to have a pram and a carseat.
Also tell his mum you need some more things for the baby still and see if she is willing to help you out. Bedding, clothes and nappies are more likely to come via grandparents i have found. But don't be afraid to ask for a baby monitor or car seat if they are things you haven't got yet.
As far as the messages, upsetting as they are you have to ignore them and accept yes he probably was drunk, especially if he is making excuses for it when he is sober. Even if there was some grain of truth in it would you really want this man in your life? In baby's life is different. Ask him to stop sending them as this is a very emotional time for you and you are getting upset by it which isn't good for the baby. Say you want to include him fully as a parent but not as a partner.
Stay strong, i was on my own for the vast majority of my pregnancy after he decided he wasn't ready to be a dad. But the last month was the easiest for me emotionally as my hormones had me in a constant high.
Gilly