I've made wine at home, but it was only after I had gotten comfortable brewing and had most of the equipment.
It's not an expensive setup, but like many hobbies, there is a start up cost.
The two main things you need are a fermenting bucket and a glass carboy (a giant bottle). The ancillary equipment you need is extensive, like brushes and cleaning solutions, piping & tubing for siphoning, etc, etc, but you can get by with a little or a lot, depending on how you do it.
I bought the prepacked region-specific grape juice at the brew store about a mile from my house and I was able to borrow their filter and corker, which made things much smoother & better. The actual winemaking wasn't much harder than baking a cake - mix this, add that, let it ferment, siphon, ferment some more, add this, bottle, and then wait three months to drink. I made a few batches and they came out pretty good, if a little sweet, but they were fully consumed before having much time to age. With home wines, you don't age much more than a year, but I found a bottle at my sister's house that I gave to her the year before and it was not bad at all when we tapped it after 12+ months.
I recommend both brewing and vintning as a hobby, but it really helps to have a local brewshop to guide you and rent/borrow the extra stuff you need. With a cost of about $2-$3 a bottle though, it's just as good to buy the 3-buck-Chuck at Trader Joes.