My background is more in software development so working with electricity is new to me. A lot of the tutorials and forums I've been reading have me a bit confused so any help is greatly appreciated!
The max use should be no more than 80% of the full loads,otherwise, It‘s cause the power supply to overheat,the service life of the power supply will be greatly shortened.We recommend you to use this 5V20A 100W power supply to power devices less than 80W.
At 90W, you would be exceeding the manufacturers recommendation so don't be surprised if it runs rather hot and fails prematurely!
You would power the Arduino through its 5V pin, not the Vin pin or barrel socket. Take separate 5V & GND lines from the PSU to power the Arduino. These lines don't need to be heavy gauge because the Arduino won't draw much current (assuming it's only controlling the strip). The 5V and GND lines from the PSU to the strip should be good quality and heavy gauge because they will carry a lot of current. You will also need to feed power into the strip at both ends and ideally at least 1 or 2 places along the strip also, again with heavy gauge wire. This is because the conductors on the strip are thin and so have a relatively high resistance, which will cause some voltage drop. The voltage drop may cause gradual changes in colour along the strip, as well as unwanted heat, which could reduce the life of the strip. This is why the heavy gauge wires are important, they provide a lower resistance path for all that current. Don't forget to put a large capacitor (e.g. 1000uF) across the 5V/GND lines at the start of the strip and ideally also at the other points where power is fed into the strip.
The wire gauge should be chosen based on the PSU you use. You can find tables online which show what gauge is required to carry a certain current. Choose one that can cary all the current your PSU can provide, plus maybe 20% margin for safety. Google for "wire gauge current" or similar. These tables will tell you what American Wire Gauge (AWG) or mm² the cable should be.