What kind of wire do I need for 3 LED strips?
A rule of thumb for 3528's is 2 amps per 16ft (5m)  section.  They are rated to connect up two strips (not 3) nose-to-tail (4 amps through their internal bus-bars).  I recommend limiting it to 3 amps (1-1/2 strips) but even then you'll have noticeable fade.  To avoid it, you need feeder wire.  18AWG intercom cable is ample, as it is nominally good for 6-7 amps.  Anything heavier will be difficult to attach to the strip ends anyway.  I prefer 20. 

Option 1: Ring (no feeder)

Wire the LED strips in a total loop.  Always, black (-) to black... and red (+) to red. The power supply feeds the loop in both directions.  Yes, there are redundant current paths.  That helps carry the load and evens out fading. 

However you'll readily notice fading between the power supply location and the opposite side. 

Option 2: Ring, with feeders

Lay it out as in a ring, but also add 18-20 AWG feeder wire.  (18 AWG intercom wire probably being the cheapest choice).  Splice it in wherever makes sense - at the ends of the strip runs, or in the corners if you are cutting. 

So imagine your room is a clock face with the power supply at 12:00.  I'd run feeders to the LED strip junctions at 4:00 and 8:00.   Or if you are cutting for the corners, I'd feed there instead at 3:00 and 9:00 (wouldn't bother with 6:00). 

Since each LED is no farther than 1/2 strip (8 feet) from a feeder, there'll be no visible fading and you'll get max light out of the LEDs.