I always travel to Lindos self catering but never cook ! If you are planning to then be aware that self catering accommodation has very limited cooking facilities - two electric rings and a kettle, even a toaster if you're very lucky! So you can't really rustle up more than a salad or basic meals - that said you are normally provided with all the basics (knifes, pans, etc) to do just that. Most accommodation will have a corkscrew but often it's just the type that's attached to a tin opener so you might be better taking your own.

There's a small supermarket fairly close to Krana and several in the village aswell as a butcher and bakery.

I'm sure you'll have a great time at Krana i know a couple that won't stay anywhere else! The only downside is the steep climb back up the hill at night but in October you're out of the searing heat and a taxi costs next to nothing. ENJOY
Amost forgot - St Pauls Bay is quieter and more rocky so there's more to see if you're snorkelling but i prefer Pallas Beach for swimming as it's sandier and more facilities.

Take a decent small veg knife (in hold luggage of course!) as often the knives supplied in the 'kitchenette' are not sharp - this can then be used for fruit / cheese/ bread and to slice those lemons to put into your pre going out G&T !!
Another useful item we have found (& weighs nothing!) is ice cube bags! again for that pre going out G&T .
Take your own favourite Teabags as often they don't stock Typhoo (just Lipton Yellow label which is like sweepings up!)
We also take a travel kettle since many apartments don't have them & you can wait forever for that pan of water to boil.
Also a small supply of washing up liquid, teatowel & pan scourer is useful or you will have to buy these things .

Have a brilliant time - eat out & experience local cuisine as much as possible - it certainly saves on the washing up!