A c/section makes it a little harder for YOU to feed the baby whichever way you do it. It doesn't affect the way that breastfeeding works, but can make it a little bit more hassle because if you can't easily lift the baby you need to keep asking for help.
After a medicalised birth, the baby might be quite sleepy for the first day or two. After that they go on a mad feed fest. It is normal and good for your supply to feed every 2-3 hours including night time in the early days. I'm sorry, this is hard but very normal and you need to find other strategies for getting sleep.
Often the best thing to do (whilst DP is on paternity leave) is spend as much time resting with your baby as close to you as possible. Stay in bed/bath/sofa with skin to skin contact for hours and hours at the beginning.
If you don't feed often enough (between 8-12 times in a 24 hour period at the beginning your milk will take longer to come in.
If you have begun to feed then it is not possible for you to not have any milk when a baby feeds as it is made to demand as the baby feeds. If your breasts feel empty it just means that there is little stored, but your baby will still get milk made right then.
If the baby slows on one breast or gets a little frustrated at the speed of the flow, simply switch breasts. Do this every the baby slows until no longer interested. This is a great way to build supply.
Expressing in the first 6 weeks is not recommended as it interferes with the relationship between your baby and your boobs. Neither get the correct information about supply and demand. Also expressing is for many a learnt skill with practice and is no indication of milk supply.
Keep the phone numbers of the breastfeeding helplines to hand and phone them if you have any difficulties at all, - even if you are still in hospital. They are the 'experts', overstretched, out of date maternity staff are usually not.
HTH