Large supermarket Papantoniou has everything though we tend to just shop there for items the smaller shops don't sell and use the smaller specialist butchers/fishmongers/fruit and vegetable stores for local produce (plus I hate big supermarket chains taking over the world!)
Row of shops on your left past the school as you enter Polis from Argaka - bakery and fruit/veg shop there - both very good.
Papantoniou is 100m further on on your left - entrance opposite the "Flo" cafe.
Fishmonger is in town - turn right past the church, right again, then left past Chris Spiritis supermarket (another good fruit shop) then left again. Fishmonger is on your right and is excellent.
For wine - choose Onoufrious for red and Vasilikon for white (our favourites on the Cyprus Travel Secrets site) - stocked by all the supermarkets inc the small ones OR (if you think you'll get through a case of 12!) we'll tell you how to get to the winery in Kathikas 20mins drive away. Around £3.50 a bottle in supermarket, £26 for a case!
