Its at the top end of your budget (and perhaps a bit more), but I was talking to the laptop guys where I work (it was a quiet evening), and one of them liked the Lenovo Yogo 2 convertable
laptop things. They are touchscreen, so you can use them like a tablet, but switch them around and you have a keyboard as well. They tend to have a more powerful set of hardware than a tablet, but not as much weight and size as a full blown laptop. He wasn't keen on the 'convertable' things, where you can remove the keyboard - faffy, and because the main bit has to contain everything apart from the attached keyboard, the contects tend to be prone to breaking.
On the other hand, the smallest they come is about 11in, so perhaps a tablet would be better. The first thing we ask when a customer asks about a tablet is what smartphone your using? If you Android, then go with that, Apple, the same, etc. Using two different operating systems is a faff, and you'll find it much easier if you stick to the same OS - you just know where everything is.
Ipads are not cheap, but they sell very well for a reason - they are very very easy to use, and there is a lot of apps for them - they just work. Best thing to do is to into a proper shop and try one - if you dont get on with the OS, it will be apparent very quickly. tablets are meant to be easy - if its a pain to use, dont bother.
Have a look on Lifehackers Dealhacker of the day every so often - there are special deals that come up on tablets a lot, and this includes Argos's Ebay outlet, which can sell off returns etc relatively cheaply. But at the end of the day, the cost of a decent tablet reflects its capability.