Ok here's my 2 cents. I'm sure to a lot of people this would be wrong but it is what I would do with only $300. If you get a HPS or MH light you will need to figure out how to cool it.
So:
1) you need a T-5 flourescent light. I got my last 4ft 8 bulb on craigslist for $125. HTG has a brand new 4X4 T5, rope ratchets and a timer for $171.
http://www.htgsupply.com/Product-GrowBright-4-Foot-4-Lamp-High-Output-T5-With-Choice-of-Bulbs.asp
2)Some people like dirt. I don't and find the waterfarms generally foolproof. Next you need a Waterfarm. Now most people will tell you, you can make your own for cheaper.. You can and probably will... Eventually. But we are trying to lessen that learning curve. If you buy your first one. It will come with EVERYTHING you need except for the plant. Nutes, air pump, everything. You will then be able to see first hand how it works. Then you can duplicate it down the road. $66 at HTG.
http://www.htgsupply.com/Product-WaterFarm-Single-Stand-Alone-Unit.asp
3)Unless you have someone who will drop a clone in your hand, you need a bean or two. Off the top of my head I recommend one feminized "Reserva Privada OG Kush #18" Order it at Attitude seed bank and they will give you a feminized "Delicious Seeds Black Russian" for free. Get the coffee mug guaranteed shipping and you will be out a total of $41.
https://www.cannabis-seeds-bank.co.uk/reserva-privada-og-kush-the-18/prod_3135.html
4)You need to circulate some air. Box fans are ~$18 at Lowes.
This will eat up your $300 but you will be on your way to some bud. In dealing with hydro, you will eventually need a ph meter and a ppm/ec meter. Dont even worry about them right now. Follow the directions on the GH nute bottles and you should be good. Research the Lucas Formula when you get time.
Hope this helps.