Hey!! I did that with a 2.5 gallon...lol...but with cured live rock. You don't want uncured. Stinky stuff. It'll cause a tramendous ammonia soup in that tank that would take quite awhile to settle down for anyting to establish. Cured
LR wil have some dead things on it and is enough to start the tank on a cycle.
JMO.
Anyway...you can get a retro fit lighting kit to fit the tank. You want at least three watts per gallon, so with a 6 gallon tank, you only need at least 18 watts. There are small power compacts to fit that need. What I did for the 2.5 was put an AllGlass compact bulb that fits incandescent fixtures. It was the equivalent of a 50 watt bulb. Ask your
LFS if they can help you.
As for a filter, leave out the blue carbon cartridge and fill a filter bag with small crushed pieces of
LR. Rinse in used saltwater once in a while to clean off any built up gunk. I also suggest doing small, but frequent water changes. If you do say 2% or 3% water change daily, you could go without a skimmer. Those tanks are very small to fit a skimmer without it taking up so much room. Remember to check
SG daily too and have fresh
RO water available. Small water volume like that evaporates quickly allowing the
SG to raise rapidly. Good luck. My little 2.5 did great. All I had in there were a couple of shrimp, small crabs, some small coral and an itty bitty baby boxfish till he was sold...then a tiny angel went in there till it sold etc., etc. This was set up at the store I work for. Sold lots of tiny coral
frags for nano tanks too. It is good to have some macro algae in there to help with natural biological filtering.
Have fun