i started growing inside 3 years ago, and have a closet full of shit i had to have....at the time.
get a ppm/ec meter, a ph meter, and a small bottle of test solution for each.
if you have room, i'd go with a 4x4 tent, or even a 5x5. 3x3 is going to be just a little tight if you want to grow more than maybe 3 plants at a time.
are you planning on running a crop at a time in the same tent, or thinking about getting a perpetual going, with a smaller veg tent to start plants in and a larger tent to flower in?
if you're going to go one crop at a time, get a decent 600 watt ballast that will run both MH and HPS, then get a 3000k bulb in hps and a 5000k bulb in MH. i'd also get a t5 fixture or a quantum board with a dimmable driver to start stuff under, you don't want to start seedlings under a 600 watt light, makes em either burn or stretch like crazy.
basically same thing for two separate tents, except two drivers, and i don't think you'd need more than 400 watts for veg.
if you can afford it, go all quantum boards and cob leds from the start, save money on power, and will only need a fan and filter for odor control, not heat control. there are several excellent vendors on the forums here that have been members for a long time, and a lot of people here have done business with them. i'd suggest looking in the led forums here before you go to amazon or ebay and buy something that looks good but is actually shit.
if you have to go with h.i.d. lighting, you'll need a fan and filter. i run a 5x5 tent with 4 plants flowering at a time, and i've had to upgrade twice to keep odor under control. i ended up with a 6x24 phresh filter rated at 550 cfm, hooked to a fan that tops out at 440 cfm. i run it wide open when the lights are on and half speed when they're off, and thats the minimum i've found that will effectively control smell in that size area. so you'd need a hood (or two) i really like the 6 inch cool tubes with the bat wing reflectors, but thats a personal preference, any decent hood will do, but keep the dimensions of your tent in mind when buying a hood. you'll need hangers for your hood, and for your filter. i have an oscillating tower fan, and two small clip on fans in my flower tent. you'll need extention cords, a fan controller, at least a couple of timers, make sure they're rated to carry the load of your lights.
you need pots of some kind, medium to grow in, a watering can, or a drip system, or a blumats system....depends on how you intend to water. i would go with at least 5 gallon containers, be they buckets, airpots, smartpots, or totes. more roots equal more fruits.
you need to feed them something, i suggest Jack's dry salts, the citrus blend is good, they have a wide array of different formulations, and they're way cheaper than buying bottles of mostly water, with some of the same stuff in them.
measuring spoons....
that ought to get you started, i'm sure i forgot a lot of stuff, but i was looking at what i actually still use after 3 years of trying shit and going "well this is fucking useless"