First off, I've never heard of hydrogen peroxide being used as a bulk treatment for algae or cloudy water. Spot treatment, yes, but never just dosing the water column. If you filter's on, you subject your BB to an oxidizing agent. If you're filter is off, then the H2O2 won't get properly distributed.
Second, I find it hard to believe that anyone can set up multiple tanks and never have had algae blooms or cloudy water. Both of those are classic, well documented examples of cycling tanks establishing. I've had both almost every time, and I'm sure that most others can attest to that.
Third, assuming that its green water, you need to fix the root of the problem and not just apply some temporary bandaid. Green water is too much light intensity. It usually means that you have too strong of lights, or that your tank is getting direct sunlight from a window.
Fourth, IMO, don't cheap out on anything connected inline with a filter like a UV sterilizer. Read the reviews for the cheap UV sterilizers on ebay (usually odyssea knockoffs) and you'll see that most of them are cheap and prone to breaking, with a heavy seasoning of catastrophic failure, which you don't want with something that has that kind of flow going though it. In all reality, there is no need for a UV sterilizer in a FW aquarium. They're like roombas: nifty, but not needed. Anything a UV sterilizer can solve can be solved by good aquarium technique.
Five, if it's just cloudy water, let it be. Most cloudy water bouts are caused by heterotrohpic bacteria. Pretty much everything that these bacteria can do are good: break down fish poo, eat dissolved organics, etc. Let them be and establish themselves, they're your friends in the tank.
I've added some pics incase that helps
