on a 4000 watt amp the best gauge wire woul be between 2 and 0
The ampacity or amp rating of all wire is rated by the size of the wire. NM (non-metallic sheathing) wire is no different. In household wiring 14 gauge wire must go on a 15 amp breaker/ 12 gauge goes on a 20 A and 10 gauge goes on a 30 Amp.
Use 8 gauge wire.
# 3 gauge
You need a 60 amp breaker.
Minimum size is 10 gauge with a 30 amp breaker. To be safe I would install an 8 gauge with a 40 amp breaker.
Normally it is a 20 amp using AWG 12/2 gauge wire. But it really depends on what size wire is on that circuit. If it is white AWG 14 gauge then use a 15 amp breaker. If it is yellow AWG 12 gauge then use a 20 amp breaker.
wire gauge is used to determine the size of the wire to be installed based on the amperage draw of whatever is being hooked up on the receiving end. ie 14 gauge is for a 15 amp circuit, 12 gauge is for a 20 amp circuit, 10 gauge 30 amp etc. to get specific amp draw ratings on a particular gauge of wire look at a current National Electric code book or ugly book.
2 or 4
You should use a 4 guage wire. There is a handy chart located at http://www.the12volt.com/info/recwirsz.asp which lists the proper wire size for differing wattages.
You listed no gauge wire. This is the required breakers.14 gauge - 15 amp12 gauge - 20 amp10 gauge - 30 amp8 gauge - 40 amp
30 amp breaker with #10 gauge copper wire
NEC states that all GFCI's require a 20 amp circuit, the wire size for a 20 amp circuit is 12 gauge.