For a new PSU, anything from Seasonic lineup in 600W range will do just fine. E.g M12II-620 EVO
Why replace a mediocre PSU with another mediocre PSU? The M12ii are group regulated, and missing alot of important protections. Definitely not something you want to buy for a GTX 1080 system, especially when you can find much better power supplies for the same price.
Also, no need for 600w. You are only losing money, and ending up with a PSU that is likely louder. No advantages to choosing higher wattage. A 450w or 550w will be more than enough for OP's system. The H110M motherboard suggests their CPU isn't powerful enough to be needing a 550w power supply.
Budget PSUs include the Corsair CX 2017, Corsair CXM 2015, be Quiet Pure Power 10, Corsair Vengeance, CoolerMaster MasterWatt (not lite).
High end power supplies include the Corsair RMx, Bitfenix Whisper, EVGA G3, Seasonic Focus Plus.