[axel]

What is the best filtration method to a nano reef tank, a common filter, or a mini sump? and a refugium or just a normal sump?

[glampka]

There is really no "Best" filtration system. It all depends on what you want to keep, the size of your tank & what works best for you. When you say "nano" I think of anything 30 gallons or less. For me on my 30 gal, a protein skimmer with a DSB works great. That's not to say it works for everyone.
What are your plans for your tank? If you need a place to grow pods, then a refugium would be the way to go. If you don't need them, a sump is the way. When you say "common filter" do you mean power (HOT) or canister? Everything has pluses & minuses. Need to define exactly what you need & go from there.

[Coral]

a simple hang on filter with a cheep grow light from homedepot ($7-10). Then put in your macro algea and live rock, don't put in sand becouse it will flow out but if you must use a mesh bag