OK. A few things first...
Most folks here (me included) will suggest doing a fishless cycle. Cycling with damsels is a tried-and-true method, but all you're looking for is an ammonia source to start off your bacteria population. And the ammonia source doesn't have to be living. A good ol' cocktail shrimp from the grocery store works just fine, doesn't cost much, and won't suffer from ammonia poisoning as the tank cycles. Here's a good article:
Cycle your salt tank
Even if you were going to cycle using damsels, four in a 14g is waaaaay toooooo much. Four of *anything* in a 14g is too much. Yes... I know you said you bought bottled bacteria, but I don't put too much faith in that stuff.
Yes - you're probably seeing ich. Not good. Garlic won't cure it. You have two options: copper medications and hyposalinity. Neither should be done in your main tank. Copper will make the tank toxic to any inverts (crabs, corals, etc) in the future, and hyposalinity will kill off any inverts in your existing live rock, causing another cycle during the hyposalinity. Quarantining livestock before introducing it to your main tank is a good habit to get in to - which is another good reason NOT to cycle using fish. Here are some articles on ich and hyposalinity:
ATJ's Marine Aquarium Site - Reference - Hyposalinity Treatment
Marine ICK - everything you need to know
The ich issue is a big problem right now. The bigger problem is that even if you nurse these 4 fish back to health, they can't stay in your tank - it's just too small.
If the LFS
that sold you these ich-infested buggers (obviously they came with ich since this is a brand new tank - they can't blame YOU for introducing ich to them!) would take them back for store credit, I'd strongly suggest taking them ALL back to the store and empty your tank and disinfect it. Basically start over. I know that's not what you want to probably hear, but it really would be the easiest thing at this point. Starting off on the right foot in this hobby goes a long way to making it really enjoyable. Starting off in the situation you're in... not too much fun.
Anyway... test strips - those are fine for cycling, but you're going to want to get liquid test kits for the long term. API is a good brand that doesn't cost an arm and a leg. There are better kits, but API is a great value.
84 to 78 is a pretty big temperature swing. I'm not familiar with how folks cool those biocubes, since they're fully enclosed, but I'm sure other biocube owners will pop in tomorrow to comment. You really don't want more than a couple degree swing, and 84 is hitting that upper "danger" limit.
As far as the best chemicals to invest in for quality of water and health of livestock... there's no magic chemical. Once your water quality gets bad, it's bad - so it's best not to let it get that way to start with. Weekly testing and understanding what your tank is doing and why will beat any product that claims to eliminate water changes or make your tank instantly hospitable. The best thing to invest in is education. Read as much as you can and understand why people are doing what they're doing.
I wouldn't think about corals until you get your ich situation resolved. Once it is, give yourself 3-4 months of *stable* water parameters before you start adding corals. It will give you time to research about coral!
- large polyp stoney corals (things like bubble corals, torch corals, favia, favites, brain and maze corals... things with relatively "large" polyps)
- small polyp stoney corals (things like acropora, stylophora, montipora... things with relatively "small" polyps)
In general, but not true all the time by any means, LPS
corals are more forgiving and less light demanding than SPS