Have the following re tested;
PH (should be 8.2-ish sounds like yours is good)
Ammonia (Must be 0 Parts per million "ppm")
NitrItes (Must be 0 PPM)
NitrAtes (0 to no more than 10 PPM - lower is better - I shoot for 0-5)
Phosphates (0 ppm is desirable)
Salinity ( AKA Specific gravity - should be 1.023 - 1.025 - ish)
I know you just had it tested but you need to know more than ph & nitrates. I suggest you buy a good quality test kit of your own too, Red Sea, Instant Ocean and Salifert all make decent test kits that are affordable. If your water parameters are similar to the above suggested values, it would be safe to add a couple starter fish, like clown fish for example.
The tank may or may not need to be re cycled. Cycling in a nut shell is the maturing process where the aquarium grows the needed bacteria and micro organisms that help maintain the water quality. Depending on how this tank was moved and what was (or was not) done to preserve the living bacteria in your wet dry filter and the micro fauna on your rock and substrate you may (and again may not) need to go through the cycling process. It is good to test your water before you add anything but this test does not determine if your tank is cycled and stable. With little producing waste, the aquarium is not needing to process anything - when you add fish, you may see some temporary water quality issues while the micro fauna reproduces and matures to handle the waste the new fish are making. Because of this, only buy a couple small hardy fish (like clowns) and test the tank regularly to keep tabs on what the new fish do to the water. If after a couple weeks all is well water quality wise, it is safe to add a little more and again let the tank mature to handle the additional wast load and test regularly. It's somewhat of a balancing act, If you have "X" amount of waste being produced by your tank inhabitants, you need "X" amount of bacteria & micro fauna to process the waste. So don't add a bunch of waste producers (fish -etc.) all at once, add a little, let the bacteria reproduce to handle it and balance out, and then add a little more waste producers and replete the proses. Take your time.
Another very lengthy subject is your wet dry itself. These are decent filters for fish only systems but if it is your intention to do a coral system, the wet dry is not a good choice and will limit what you will be able to keep (coral wise) and will require much more maintenance (mostly water changes) to keep parameters right.
Don't run your actinic lights (the blue lights) 24 / 7. THis is playing a roll in the algae growth. Since the tank is technically newer (biologically speaking) keeping the amount of time per day the lights are on to a minimum is advisable. Probably somewhere in the area of 6 - 8 hours per day is fine. As the tank matures and you get photosynthetic organisims growing in your tank, the photo period (hours per day the lights are on) will increase. If your light bulbs are a year old, they are over due for replacement. Old light bulbs encourage undesirable algae growth, this also may be contributing to the algae you have had. Depending on what type of lighting system you currently have, you may only need new bulbs. (what kind & wattage do you have?)
Be careful using purple up or any other similar supplement. Testing your alkalinity and calcium values are the only way to know that the amount being added to the tank is correct. The volume of water your aquarium holds is not what determines how much you need to be adding (although it probably says that on the instructions). Compare this to fish food, how many gallons of water you have has nothing to do with how much fish food needs added to your tank - how many fish you have and how quickly they consume the food is what determines how much food you add. It is the same for supplements, right now you may not have much using up the buffers and carbonites your adding so it possible may be overdosed. As the tank matures and you get more and more organisims using up the supplement, you will accordingly need to be adding more - make sense? A good rule with this type of this type of thing is to test the results of what your doing.
Wow that's a lot....don't let it overwhelm you. It gets really easy after you've done it a while....Hope this helps and please ask away with any questions...Joel