Running two new circuits to outside backyard (One for swimming pool)
Two circuits to the same place must be different.

You can't simply run two 120V general-purpose circuits to an outdoor location or outbuilding.  There must be something that makes one circuit different from the other.  For instance it can be a different voltage (120 vs 240 vs 120/240 split vs MWBC)... Or differently controlled (always-on, on a manual switch, pressure switch, timer, etc.) 

For instance you could have a 240v pump working off a pressure switch, a 240V always-hot circuit powering heater on a thermostat in a shed, a general purpose 120V circuit, and two lighting circuits controlled by different switches.  

Separate neutrals required; shared ground is fine

In fact, certain types of conduit are permitted to be used as the ground wire.   The ground needs to be sized for the largest circuit. 

Upsizing wires is a good idea for these distances

It's not required to upsize wires for long distances, but it certainly helps machines perform better and reduce breaker trips.  

Once you commit to 12 AWG you might as well breaker for 20A.  

No more than four

You can have a maximum four circuits per conduit.   240V/120V circuits count as one circuit.  MWBCs count as one circuit. 

If you want to have more than four circuits, you can do up to ten if you bump all the circuits up a wire size (well, 2 sizes, 12 to 10 etc.).  This applies to circuits up to 20A.  For larger, the math is more complicated.