LED Strip setup on stairs. Unsure which power supply will work for 1200 LEDs
WS2812B LEDs are a lot of fun, and fairly easy to handle. That said,


  Would any gauge wire be fine for this?


NO!!!

You need a wire large enough to carry the current without too much voltage drop. All wires have some resistance, which means the voltage drops over the length of the wire. According to Ohm's law, the more current flowing through, the bigger the voltage drop. 

The WS2812B module contains 3 LEDs(Red, Green, Blue) with each color drawing up to 16mA according to this post https://www.disk91.com/2014/technology/hardware/ws2812b-leds-current-consumption/comment-page-1/

assuming you have 60 LEDs/m, 18 strips of 1m, that give you 60*18*3*16 = 51,840mA or about 52A max, which is no joke. This is if you turn all the LEDs to white at full brightness.

Your description is not very explicit on this point, but if you try to daisy chain all the strips, it is not going to work. Only the data wire needs to go from the output of strip N to the input of strip N+1. Power needs a more direct path.







simulate this circuit &ndash; Schematic created using CircuitLab

If you try to build that power path with a single set of wires, you will need 2*(2.5+17*0.3)=15.2m of wire carrying that big current. Of course this is an overestimate, since strip 1 will reduce the current in the wire by about 3A at 2.5m, strip 2 by another 3A at 2.8m, ... and so on. Weather you want to do the actual math or not, that means thick wire. My recommendation would be no more than 1V drop over the entire length (in theory the modules work down to less than 4V) or about 60mV/m. at 60A this means 0.001 Ohm/m or AWG 5 !!! It is gigantic. Less conservative estimates might give you up to AWG 8 ... 

An other strategy can be to have one set of wire connecting each strip directly to the power supply. This will be a cable management nightmare, but allows you to use smaller wires. 3A, 15m, 1V => 0.02 Ohm/m => AWG 18 to 21 (same computation as above)







simulate this circuit

Of course, you can also have a hybrid approach, with one wire power a few led strips instead of a single one. By now I hope you get how to compute things. You could also have multiple power supplies (one at the top of the stairs, one at the bottom) reducing the length of the wire. You could increase the voltage in your supply wire and have a localized step-down transformer for each strip. Or a bunch of strips. 

Possibilities are endless, but always remember Ohm's law!