instead of running solid pvc pipe (white or gray) at local hardware stores. see about black poly hose (comes in a large roll say 3 to 4 feet in diameter) it might be easier to pull the wire through it. along with putting the hose into the trench. let the hose snake back and forth some in bottom of trench (weave back and forth) so any settling / movement of ground through frost heaves will not put extra strain on hose and electrical in it. if you un-wind the hose and leave it set outside for a day in the hot sun. generally the curves in pipe will go away making it easier to drop the black poly hose into the trench.
get the electrical to depth or deeper, if memory serves 2 feet depth or 2.5 feet depth for my area (central IL), but you may need to be a little deeper for frost zone were you live.
you say you do not want 220, but really it be easier atleast for me a diy bozo. to run a 220 30amp breaker at panel in home. and then run wires out to shed, and install a 30amp breaker panel there. and then split off to individual 15amp and 20amp circuits (lights, and outlets)
call around, local hardware stores were 1/3 to nearly double the cost of a local electrical supply wholesaler in my area for the wire i needed. for running 60amps out to shed i think length was around 120 to 150 feet.
i bought each wire separately, and then took some electrical tape and taped all wires together about every 4 feet (2 hots, 1 netural, 1 ground) and coiled them into a single bundle, and then pulled all 4 wires together and i think i had my mom just seating there with gloves on covering the wire with dish soap as it feed into the end of the pipe, while i pulled. i did use shop vac to suck some kite string through initially with a rag tied onto end, then pulled larger rope through. then pulled a larger cable through, then finally pulled all the 4 wires together. it went smoothly but a bit messy.
when pulling wire do not wrap wire around hands and/or make sharp kinks in it. i ended up using my shoulder (wire going over it) and pulling. and also half U shape around belt area of my body. to get a grip on it. to help pull it through.
to note it, i did go with copper, when looking at aluminum wire, and diameter. i knew my wimpy body was not going to be able to pull the aluminum through any pipe. that and my luck i would of ended up with corrosion on the ends were they connected to the breaker panels. copper cost a little more but worth it.
wire needs to come out of the house above ground. and then a pipe entering the ground. then once at shed, electrical needs to come out of ground in a pipe, and then enter shed from the outside above ground.
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air compressor, fridge, freezer, various tools more so drills and hand saws, table saw, window a/c conditioner, fan/s, battery tender/charger, and more so car jumper/charger. upgrade the amps if possible it costs a bit more. but worth it.
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if you are out of your league. dealing with 220 and dealing with all the electrical. you might work with a local contractor. and see about putting in trench yourself and pulling in the wire, and leave the hookup to local contractor. and then go from there.
rent a trenching machine. it is worth it! or a small mini ex (mini excavator) for the trench digging, if going through a rock driveway, and/or some trees are nearby, you might need a backhoe/ excavator to get through the rock and/or tree roots. the chain saw like trenching machines can get hung up on rock and roots. they can handle some size, but....
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if renting a machine to put trenches in. get some more black poly pipe. 3/4" to 1" inside diameter. and run water out to shed. electrical and water lines if memory serves need to be 4 feet or further apart (horizontally), and i want to say water needs to be 1 to 1.5 feet deeper (vertically) than the electrical. when both are being ran parallel to each other. do not run them in same trench!
if you want internet or say cable tv or satilite tv out there, or an old land line phone. i want to say you can run the cable 8" or 12" above the eletrical, by code (do not quote me on that) been to many years.