I recently did my first wine kit. Most of them are 6 gallon kits.
I'm not expert, but here is my advise based on the one kit I have under my belt...
Wine from a kit is REALLY easy, but there is one thing that you have to worry about with wine that isn't a problem with beer - headspace. You don't want it because of the risk of a particular type of infection. You can either use something like sanitized marbles to fill the last 1/2 gallon or you can get some 6 gal carboys.
The kit I did required a secondary and a polishing vessel. I plan to have wine going pretty much all the time, so I picked up 2 6 gal carboys. It's also nice to have something to stir with -that you can get in a carboy. These work well
For a corker, I got one of these
. It's cheap and easy. Soak your corks and use a rubber mallet with this corker. It works pretty good.
I also got a bottling bucket and bottle filler because I never bottled before. You probably already have those.