What exactly does a graphing calculator do? In the UK, they're not terribly common - I did my degree with the same calculator I had in school plus Excel.
The standard calculator for undergrad chemistry tend to be the Casio-FX-83GT. Some people went for graphing calculators (TI-84) but they were in the minority as its not a particularly useful function and its expensive to replace when some moron in a lab spills some chloroform on it and it melts the buttons into the case. If you think you need a graphing calculator avoid the TI-84, the product simply isn't worth the price. Texas instruments cornered the market in the US and then just coasted.
Nope. Not worth it and you don't need one at all. They also aren't allowed in exams.
You will however NEED a scientific calculator like these:
http://www.amazon.co.uk/Casio-FX-83GTPLUS-S-UH-FX-83GTPLUS-Scientific-Calculator/dp/B001O3IF9U
http://www.tesco.com/direct/casio-fx-83gt-plus-scientific-calculator/210-0796.prd
This Casio one is probably the best to get since most people and teachers use them and you can get help on how to use them if you don't know how. And just look at the good ratings.
You'll certainly want it for Chemistry - I'd suggest if you're not certain it'll be with you on time that you get one from Tesco or somewhere like that (WHSmiths for example) - doesn't even need much special functionality but something simple!
If you want something to last a bit longer, I'd suggest one of these - I've had mine since year 7 (year 11 now) and it's not failed on me. http://www.tesco.com/groceries/product/details/?id=255451418 (Or Amazon: http://www.amazon.co.uk/Casio-FX-83GTPLUS-S-UH-FX-83GTPLUS-Scientific-Calculator/dp/B001O3IF9U/) you could always sign up for the Prime free trial and use that - order in the next 22hrs from this post or so and you'd get it on Tuesday