Outdoor shed (Electrical help)

Hello all. I have an uninsulated shed right next to my fuse box (outside). I wanna run power to it, I just needed some recommendations on whats the cheapest way to do it (and safest too). I want to have 3 sections in it, flower, veg/ mother room, and a shelf for a T5 and clones. I will probably have a 600 HPS in the flower tent, have a 290 Watt LED in veg/ mother. Sheds about 5X5X6. Want to use one large carbon filter to exchange air in the shed (about 200 watts I guess). And there's going to be one window/ portable A/C unit (I guess about 700-800 watts). How many amps would I need? I only wanna do 120V in the shed, and have a few receptacles in there. Thanks for the help.

bare minimum, you might be able to get away w/ 1 20 amp circuit & 2 outlets but adding a dedicated 15 or 20 amp circuit for the AC would be a very good idea.How to get from shed to breakerbox? you could go underground,they make direct burial romex. if you plan on pulling it up in a few yrs,regular romex should survive 4-5 yrs. pvc pipe is another option but dont run romex, use thhn(another wire type).yet another option would be overhead & that could be done w/ thhn type wire as well if the run is under 50 feet.
anyway around,use a GFI breaker for each run.

1 20 amp circuit would really be pushing it.. You are better off running 2 20 amp circuits out there...Bury it underground (6 inches is ok as long as nothing hevy will be driving over it) in schedule 40 pvc (plastic pipe). 1 inch is plenty big... You will use 12-2 with ground for these 2 circuits. The reason im advising you to put 2 circuits out there is because a 20 amp circuit is rated to run about 1900 watts continuous, with the ac, your hps,t5,s,fans...ect... you would be pushing that rating. Not to mention if you ever want to add anything else you would be set.... Im an electrician btw...lol...

mrmadcow stated a good idea about putting the ac on a dedicted circuit, basically the same thing im saying...2 circuits...

I had to put my ac on a different circuit indoors, theyre all 15a. Sucks too, I have to have an extension cord running out of my closet. If it wasnt such a bitch id definitely have 2 circuits. So I agree with ^^^^those guys