I always use corks for my reds.
I haven't done any white kits but you would get away with using screwtops you could even use 1l plastic bottles.
Have you tried any of the supermarket white grape juice (wow) recipes these produce pretty decent whites.
As for the reds your probably better going for one of the more expensive kits like beverdale, kenridge or vintners reserve. There are others! Not sure how much a six bottle kit would cost but the brands i mentioned come in about £40 for 30 bottles