Fine grain aquarium sand or pool filter sand is suitable for Axolotls. But bare bottom would be better- juveniles can swallow a bunch of sand and if they're still quite small it can be bad for them.
As for filters, make sure the flow isn't too strong. A simple sponge filter is great for an Axie tank, and cheap. HOBs work but aren't ideal, and you'd have to baffle the current. Internal filters can heat the water and aren't the best choice either, but can be done.
A ten gallon is going to be TOO SMALL for two Axolotls. I'd get a 20 gallon long.
The 'stuff' to take the bad things out of the water is aquarium dechlorinator and is essential to keeping any kind of aquatic animal. Never use water straight out of the tap.
I also suggest you read up on Aquarium cycling (this is
VERY IMPORTANT!) and get an API liquid test kit, as your levels are going to be all over the place since your tank is new. Test your tank water regularly for ammonia/nitrite/and nitrate as they are all toxic to aquatic life.
Scales Tails Wings and Things, What is Aquarium Cycling? How to Cycle your Tank
A few more things you'll need to know:
-Axolotls don't like light. Don't have a light on the tank and give them plenty of places to hide! They have no eyelids, they need some dark places to hide.
-Axolotls need to be kept at water temperatures of 16-18c (or around 60-64 F).
They must be kept cool! Room temperature is
not okay and leaves them open to disease and heat stress. Chillers or a fan can be used to cool your tank.
-The best diet for them is as you've figured out, worms. Juveniles can eat frozen bloodworms too.
Phew, I think that's it.