Winemaking needs less equipment than brewing but is far less forgiving about measurement. A hydrometer and a clean vessel will get you most of the way. What separates a good batch from a vinegary one is usually sanitation and sulphite management rather than anything exotic.
Adjust the must before fermentation, not after. Acid, tannin and nutrient additions are straightforward while the sugar is still there and the yeast has not started. Correcting a finished wine is far harder and rarely as successful.
Fining and stabilising are the last decisions. Bentonite drops protein haze, campden protects against oxidation and spoilage, and oak — American for vanilla and sweetness, French for spice and structure — adds the character barrel ageing would.
Then leave it alone. Wine improves with time in a way beer does not, and the most common home winemaking mistake after poor sanitation is drinking it too young. Rack it off the lees, keep it topped up so there is minimal headspace, store it somewhere cool and dark, and taste it every few months rather than every few days. Six months in a demijohn will do more for a red than any additive on this page.