I have a shed that has outlets wired with either 14 or 12 gauge wire and 15 amp receptacles. I already know that my total usage will be almost 30 amps. If I use a #10 on the first receptacle and a 30 amp breaker, can the other outlets use 12 or 14 gauge wire? Or do ALL the outlets have to have #10 wire? Can I even still have 15 amp outlets or do I need 30? I know next to nothing about wiring.
This simply will not work. The only receptacles you are allowed to put on a 30A breaker are 30A receptacles. Those are unfit for your purpose.
Further, if your expected loads are near 30A, you should be derating this by 125% (37.5A) and provisioning that much power - I.E. 40A. And they don't even make 120V/40A receptacles.
The right way to do this is to fit a sub panel at the shed, and have individual circuit breakers protecting each #14 or #12 circuit.
I am also concerned about what your feed cable is to the shed. This too will be a limiting factor in your total possible load. There are ways around them, but you should not use those ways until you are well past mismatching sockets, wires and breakers.
Sorry, but NO
The breakers protect:
- Wiring - A 30A breaker can have 10 or larger. You can't have 14 (15A) or 12 (20A).
- Receptacles, switches, etc. - Everything needs to be rated to match. You can't use a 15A or 20A receptacle on a 30A breaker because if you had an overloaded device (not planned - malfunctioning) that pulled 30A, it would melt the receptacle but the breaker wouldn't trip to stop it.
- Devices - lights, appliances, etc. are rated based on the amount of power they normally use and what they can handle when things go wrong. A device designed for a 15A circuit could have a malfunction that caused it to pull 25A of current expecting that a breaker trip would stop it before it caught fire, but on a 30A breaker that doesn't happen.
Note that this "always match" rule does have some exceptions regarding 15A & 20A - a 20A circuit (breaker with 12 AWG wire) can have 15A and/or 20A receptacles. Similarly, a typical device designed for a 15A circuit can be plugged into a 20A receptacle. But generally speaking that is the main exception and you can't mix 20A and 30A.
In case you are wondering, in addition to the "device" problem, there is also the idea that while you know exactly what is going on and what can be plugged in where, etc. the next owner (or even just a visitor) may not realize the limitations and try to plug in too much stuff at one time and end up with a fire. Code is generally written so that anyone encountering a particular item (e.g., a 20A receptacle) will be able to expect specific safety rules to be followed.
However, you have an expectation here of needing on the order of 30A total current, presumably at 120V. There are a number of possible solutions.
Multi-wire Branch Circuit (MWBC)
This is a neat "trick" where you have 2 15A or 20A circuits sharing a neutral. Using 20A and 12 AWG wire connected to a pair of breakers, you can wire things up so you have 2 circuits instead of one. Actually it isn't two-for-one, more like two-for-one-and-a-half, because (ignoring ground) you use 3 conductors to get twice as much current as 2 conductors. It can be tricky to install properly, but in limited circumstances can be a solution.
If you bring in 30A to a subpanel then the subpanel can have multiple 15A or 20A circuits connecting to individual breakers in the subpanel. Even better, if you bring in 30A @ 240V (hot/hot/neutral/ground) then you actually get 60A of available power at 120V, which should be more than enough based on your question.
Either of these solutions is dependent on being able to run the correct wire (i.e., 10 AWG but the correct # of wires) from the main panel to the shed, and proper installation, including grounding (you may need ground rods as well as connecting the ground wires correctly). Not a trivial task, but if you provide more specifics about what you have currently have and what you are able to do in terms of changes to the wiring, we can provide more help.