In my opinion there are two things against screw tops, they generally have a waxed or plasticised cardboard disc as a seal, designed to be used once and then thrown away, this could present a source of infection. Also, unless you've racked your wine, stabilised with sorbate and are absolutely certain that fermentation has finished, screw caps can't blow off.
If you throw away the screw caps and use corks, you might find you need a larger diameter cork.
Personally, I wouldn't bother with a corker, I tend to use plastic stoppers, around 5p each and they are re-usable after a quick soak in a sterilising solution.