Since I'm new to beer brewing but have been making wine for over ten years, I figure I should at least help out where I can
Wine is easier to make than beer. And aside from the filtering process (although you can get a decent filter for under 100 pounds), less exspensive. Using fruit or even bottled juice (add a grated appple to the liquor if you're using juice - the yeast needs a 'floatation device' in order to swim around properly) is easy. I make only wine from wild fruit, so the raw material is free, and it has the bonus of getting me out and moving.
My tip is to use only pure strains of yeast when you're starting out. The expected end alcohol is stated on them, so you really don't need to measure the specific gravity at all. A little vinometer is sufficient - and cheap. I always have two or three on hand in case one breaks. You'll want to have pectinase and lactic acid on hand. And sugar (unless you really are using only grapes). The pectinase prevents the fruit from gelling and breaks it down better, the lactic acid brings down the ph, which is especially important for fruit with little acid, e.g. bananas, blueberries, etc. Fruit with high acid content (cornel cherries for example) is quite tricky, so don't start out with anything like that.
I generally make 20 l batches (150 l for apples), and my rule of thumb is 10 ml pectinase, 60 ml lactic acid max. I usually use either port wine or sherry yeast. When the initial fermentation has stopped, I test the liquor with the vinometer. If it's under 13 % (for port wine yeast), then I add roughly half the sugar that would be necessary to bring it up to 13%. Wait until fermation stops, then do the same thing over. Once it's up to 13 % (the theoretical maximum tolerance for that kind of yeast), I wait a couple of weeks - as has already been mentioned above. Very prudent.
Then you are ready to filter and bottle - or just leave the wine in the DJ (make sure you keep the water in the airstop replenished) and drink it from there (don't stir up the sediment!).
Cheers!