Hey there and welcome to the forum.
First off, I have to say that a 1g is definitely too small for a betta (unless you want to be changing the water 100% every 2-3 days). I would put it aside for now, it would make a fun project for the future (you could keep some plants, snails and shrimp in there after your betta is established.
For best results, I suggest you consider a 5g tank. The bigger the tank, the more margin for error there is. But a 5g is still a nice size.
I also strongly suggest you cycle your tank. If your 10g is already cycled, you can simply use some of the bacteria from the filter. For this reason, I will advise you against gravel... it is really difficult to clean with a siphon and shows a lot of gunk and dirt.
Guppies will eat your own fry, so I don't think your population will get too out of control unless you trap the female when she births and separate the fry.
Don't buy bettafix... it's a really controversial product because the primary ingredient (tea tree oil) has been shown to damage the labyrinth (air breathing) organs of anabantiodine fish. It is basically a watered down version of melafix and pimafix.
On that note, the best medicine is prevention. Never medicate your fish unless absolutely necessary... meds do more harm than good unless as a last resort IMO.