#12, 12 aug, or 12/2 are all rated for 30 amps. #14 is rated for 25. usually these are the 2 most common wires used in houses. chances are that the power in the shed is for the overhead light and the outlet. plug something into the outlet and turn on the light. then switch breakers until you find the one that shuts off the shed. then, with the breaker in the off position check other outlets and lights in the area. might be that the shed is tied into the circuit as some outdoor lights or a pond pump or outlets in the garage.
sounds like you plan on growing there for a while. best bet is to get an electrician out to the house and have him install a 40amp subpanel. it would actually only cost you around $300 and you'd be setup for anything you would need in the future. a subpanel is rated for 240v. so if you have 40amps at 240v you have 80amps at 120v available to you. that's more than enough to run a 4 1000w in flower, 1500w in veg, and everything else you'll need. it is always recommended that you never use more than 75-80% of the rated amps for a breaker. so, in a 80amp shed you could hook up 64amps worth of equipment.
lights will most likely be the largest electrical item in your room. then you have any a/c units and dehumidifiers. inline fans don't draw much; it's really more like 2amps for a high output 8" fan and 1amp for a high output 6" fan. 1000w lights use about 9.5amps, 600w lights about 5.5amps, and 400w lights about 3.5amps. a/c units can pull up to 10amps for bigger units. will all depends on your environment, how many lights you are using and if you air cool your lights. the rest of the stuff will be minor; wall mount fans, pumps (for hydro), meters and controllers, etc...
since you already have power in the shed it will be easy for the electrician to use that existing wire to pull in some heavier cable for your subpanel. then he'll just swap out the breaker on the panel for a 240v and setup the panel in the shed. from the panel in the shed you just tell him how many outlets you want and where. use 30amp 120v breakers and 12 gauge wire for your outlets. figure out where your ballasts are going to be and how many you will have. you can put 2 ballasts on one outlet as long as they are less than 80% of that breakers rating. meaning, don't put 2 1000w ballasts on a 20amp breaker. if you are going to be running more than 2 lights then get yourself a light controller if you want. it works just like an outlet or subpanel just for your lights. you hook it up to a 240v breaker on your subpanel and plug all of your ballasts into it. then you only have to blug that 1 box into a timer. if you have lights in veg and lights in flower and you want them on the same box you just get a controller that has dual trigger cords. then you have 1 outlet for your ac and/or dehumidifier. if you have a minisplit ac then that will go on a circuit by itself. then you have a 30amp 120v breaker for the rest of the outlets in the shed. you won't need more then that. and it leaves you plenty of room incase you have to plug some other equipment in lke a vacuum or something. you can even split the rest of the outlets between 2 30amp breakers.
good luck bro. let me know if you need anything.
