Once I have rented a film on iTunes, does it appear on a list for me to view or do I have to remember the films I've rented and access each one through that route?

Films that you rent (or buy) on your iPad should download into the built-in Videos app, you don't need to remember them or use the iTunes store app to view them.

You rented the film directly on your iPad ?

Then it should have downloaded into the Videos app - there isn't a 'rentals' tab at the top of the app, nor does it show under Movies ? You could also try searching for it via the spotlight search screen : pull down the centre (not from the very top of the screen) of the home screen in iOS 7 ; swipe your first home screen to the right in iOS 6 and below.

When you start to play a rental you have 24 hours, 48 hours if not in the US, before it expires - so if the search screen finds it and you tap on it and start playing then you will start the timer on it.