Hi
I haven't had a baby yet, so what I say comes from reading and from ante-natal classes (NCT and a private ante-natal workshop that I attended).
Once you give birth, assuming everything is fine, the MWs to VERY MINIMAL checks on the baby (basically is he breathin and responding) and hand him/her straight to you (you can request to have the baby cleaned, but the "in vogue" thing is to have them as they are: since the sticky stuff on their skin is supposed to be VERY good for their skin - removing it encourages the skin to dry out - it is better for it to be naturally absorbed...).
So, within a minute or two, the baby should be placed on your chest. Their natural reaction may be to serach for your nipple and try to feed... (although not all babies will). They wont be able to feed "properly" because you will only have Colostrum (and not proper milk). But it is always a good idea to encourage them to feed - if that is what they want.
Whilst all of this is going on, the MW/Obstetrician will be checking you out - this generally takes quite a bit longer than the baby. You need to deliver the placenta, then the midwives need to check you for bleeding, they need to stitch any sizeable tears/episiotomy (it is really quite common for women to need stitches), check the placenta etc (to make sure that you haven't retained any). This will take a bit of time and will need to be done before you can get up and have a shower.
Also midwives/duolas etc are very hot on the topic of "the golden hour": this is the hour immediately after the baby is born and when the baby is most alert (probably more alert than they will be for days/weeks after the birth). This is THE best time for bonding and stimulation with his/her parents and a GREAT time to try to pick up latching on (first feed). You wont get this hour again....
So in reality, although - at the moment - your thoughts about after the birth are "get a shower and get into some clean clothes as soon as possible"... when the time comes, things will probbaly be quite different... You will likely be knackered, not keen to move, unable to move (because you are still being checked out and maybe stitched) and you will be completely caught up with your baby (just wanting to take everything about them in and not let go of them...
).
As I said, though - that is from what I have been told and not personal experience...
I would say, go in with an open mind and "go with the flow". You are unlikely to be in a rush for a shower afterwards: take your time, enjoy that first hour with your baby and - if baby's instinct is to try to feed - why fight it? They say, with newborns, that it is best not to ignore their needs.
QT