Melafix is mostly tea tree oil which has been known to coat the labyrinth lung organ of bettas and cause them to suffocate, so most people won't use it. This oil has natural antiseptic properties, but it's not a real antibiotic. It would be like putting neosporin on a cut to prevent infection. It's not going to help with anything serious - anything that very clean water and time and maybe a little aquarium salt wouldn't heal right up. Some people use to to prevent infection where fish have become injured.. that type of thing.
BettaRevive is a combination drug cocktail of many random drugs meant to treat many random things, with the intention of treating most anything. The drugs included are toxic and harsh and they're just kind of a "throw all" at it approach and hope something works. It's much better to actually diagnose the fish and get them a drug or treatment that will actually approach the given problem, not just throw a bunch of stuff at it and hope something works and nothing hurts.
It contains:
neomycin sulfate - antibiotic good for gram negative but not gram positive infections
methylene blue - mild parasite and maybe a little mild anti fungal
"proprietary polymer mixture, buffers, EDTA" - no idea not meds
malachite green - harsh and toxic external parasite treatment
cyanocobalamin - vitamin b12
electrolytes - probably salt but who knows
I would always have on hand:
* A hospital tank setup, meaning something around 1-2.5 gallons that could be kept warm by some means, either a proven and tested heater, floating in a larger tank you already have set up, or in my case I keep a fish room a constant set temp which will keep the fish inside the room around 78 degrees without using a heater.
* Aquarium Salt:
http://www.petco.com/product/1697/API-Aquarium-Salt.aspx?CoreCat=OnSiteSearch
* Epsom salt (pure 100% magnesium sulfate with no additives or dyes of any kind):
http://www.cvs.com/shop/product-detail/CVS-Epsom-Salt?skuId=215202
* Extra plastic solo type cups to help with medicating and water changes
* Kanaplex (or other Kanamyacin based product):
http://www.drsfostersmith.com/product/prod_display.cfm?pcatid=24795 -> because this can be hard to find and some diseases it can treat need very fast response times.
Other stuff that you may need would either be more readily available or at least not require instant response time. I also personally have the following on hand:
* Prime
* Stress Coat
* Metronidazole, Focus, and a crappy wheat based pellet good for soaking:
http://www.drsfostersmith.com/product/prod_display.cfm?pcatid=4264 and.. the site is down so I can't link :S Server overload.. hmm..
* Prazipro