I went to Zante last year- Laganas, which is very close to Kalamaki.
There are always loads of supermarkets around the resorts where you can stock up with your food- some of which you will more than likely recognise!
We had quite a cheap apartment, but it was still well stocked with cooking equipment etc.
If you buy any salad, vegetables or fruit- dont forget where you are & wash them under the tap- make sure you use your bottled water.
Its great not to be commited to your hotel for meals- there's lots of restaurants about that cater for ALL tastes- English, Chinese, Indian, Italian- and prices were quite reasonable too.
Zante is famous for its turtles & has some designated beaches that are Marine National Parks. The main beach between Laganas & Kalamaki is one and you are not allowed on it between 7pm & 7am- so dont do what we did & get stranded halfway along at 7.30pm only to be told to turn around & go back!! It is beautiful though.
My only dislike with Greece is the sanitation issues- they don't have the most sophiscated sewerage system & occasionally some streets smelled.
(and you cant flush your toilet paper into the loo- you have to pop it in the bin. Which can be a bit unpleasant & takes some getting used to!!)
Outside of all the bars & restaurants there were PR agents who try to lure you in. This used to happen on Spanish Islands, but I think its been stopped now. The best thing to do, if you're not interested is to just keep walking, be polite & say "No Thanks". They are only doing their job- but they can be annoying!! Unless of course you want to go into a particular place, in which case, haggle with them for some free drinks!!
I really can't think of anything to suggest you take- you can buy anything you might need whilst you are there- thus saving space in your luggage.
Hope you have a lovely holiday.