you can quickly do the math with watts and gauge like this (i presume youre american, by the gauge measure of wires):
power = voltage x amperage (current)
max power for that relay = 120V x 10 = 1200W or 1.2 kW
your demand = 2 x 600 watts + 2 x 315 watts = 1830 watts
my recommendation = 2 relays, on each 1 600w and 1 315w lamp, so total is 915w and safe under max 1200w of power that relay can take… if those are lights for different rooms, so spacially your 600w and 315w lights are divided by some distance, i would put 600w on each relay to avoid putting 2 x 600w lamps on relay (maxing out), and 2 x 315 on one, so in total 3 relays… always rate your fuses and relays to be higher than you need…
about wire, eh, you americans are special… you will see numbers as low as 3.7 amperes, but that is over conservative imho, and here i found this chart: https://www.engineeringtoolbox.com/wire-gauges-d_419.html that says 15 A which has more sense for me, but if you can tell me from what state you are i can find the right gauge needed… anyway, if we follow that last number, which is also around same number that is used in Europe standards, you can use that wire for devices up to 1800w, but again, that is maximum, and i would recommend keeping this up to 1500w… how does this help you? well, for your total power usage, you need at least 2 power outlets (check edit), and to have 2 relays, on each 1 x 600w bulb and 1 x 315w bulb, or, you have 3 relays, on one outlet 1 relay with 1 x 600w, on second outlet 2 relays, one has 1 x 600w and other one has 2 x 315w bulbs… does this make sense? if you can tell me how you will power this (how much outlets you have), i can make a diagram for you and give you some tips with wiring (if you have only one color, you can still use it, but you have to mark each positive and negative etc.)
edit: i just saw your rig, give me a sec to check it out… i was wrong about outlet number, somehow got mixed up in my head about it, i would need to know what is maximum power draw trough your outlet, maybe you can draw all the power from one if your circuit supports it, but you would need to go to your breaker room and find the one for the room and outlet youll connect it to, so i can tell you more…
edit nr. 2: ok, like that you have 4 relay board, im gonna draw something fast…