Nice start! Seriously. I know your first round of livestock died, but that happens in this hobby.
The red algae you're referring to is cyano bacteria, and you're right, you probably dropped the oxygen levels in your tank when you used Chemiclean, and this could have started the killing process. Cyano means excess nutrients, and it likes to cling to areas of low flow. So, often times increasing flow in these trouble spots can help eliminate the cyano problem.
Here's what I would do:
Don't by a Damsel...unless of course that is the ONLY fish you want in your tank. I'm serious.
Put in ONE turbo snail.
Put in about 2-3 Astraea snails.
Put in about 2-3 hermit crabs (make sure they're reef safe hermits. Some aren't!)
Maybe add one or two more other snails like Nassarius or Cerith or whatever other beneficial species you can find.
Now, the goal is to keep all of those occupants alive. If a bunch of snails die the first two days, you're going to get a nutrient spike again, but at least you'll only be losing $5 instead of $35. So, just start with snails and hermits. If they live 3+ days! then your water is habitable. At this point, you'll need a fish in the water to provide poop for the clean up crew to eat.
Now pick your fish. I'd recommend a clownfish. Maroons, Tomatos, and blacks, are the more aggressive clowns, so just know this.
After you add your fish, I would do TWO 10-15% water changes a week for at least two weeks. This should help balance out your water while your bacteria colonies struggle to keep up with all the bio load you just a added.
Once your clownfish and basic clean up crew have managed to live for about a month, it should be safe to start slowly adding more things, one or two at a time. Remember, even corals add to your bio load.
Here's a cheap secret. Once your basic clean up crew and one fish have managed to survive, just wait until you see a decent amount of coralline algae growing on your rocks. Coralline is a sign of stability, and should indicate that your tank is ready for another coral or two. You're new, and probably shouldn't follow my tactic exactly, but I NEVER use test kits on my new tanks. I just start with a cheap clean up crew, and then I wait for coralline to grow before I start slowly adding fish. This is a risky and imprecise way of doing things, but it works for me. You really can learn a lot about your tank just by staring at it every day. Test kits are handy, but not an absolute necessity.