Laptop. An iPad or any tablet is a great addition to a home pc, but not a replacement.
To type anything on an iPad you have to have the iPad flat and hunch over it; much of the screen will be used for the onscreen keyboard.
Unless you have a gadget to prop it up, you will have to hold it at an angle to suit you, and it is not really that small to hold comfortably with one hand.
The hard drive storage will be not be as big as a laptop; there is much less connectivity such as usb ports, hdmi port, memory card reader; no cd/dvd drive; less powerful; smaller screen...
As you will not be carrying your machine very much I would go for the largest screen I could afford. The keyboard will be larger and more comfortable.
This is a true desktop replacement within your budget
Amazon.co.uk User Recommendation
and is more than good enough for your needs. There is also a Toshiba machine similar spec and price.
Go to PCWorld or suchlike and have a good look at the laptops to see what sort has the best keyboard for you. I like the scrabble tile type, others don't.
Buy a computer magazine and read the reviews and specs so you can get a good idea of what is available now. Then shop around. Amazon isn't always the cheapest; look at Argos, John Lewis (really); Tesco Direct and even the big chains such as Dixons and Comet.
There is a massive choice in your budget. Decide what you need the machine to do.