I think I am going to try for a 10 gallon tank soon, my parents are moving me to a different room in the house so I will have a lot more room for them.
And I also asked my mom about the 10 gallon, she said we could purchase one soon for my Black Moor when he got bigger (when the guy at the store said it was needed) but I'm sure I can tell her now I will buy my own quickly so my fish won't suffer, I won't make the same mistake. 
And so I need sand or is gravel okay? Also, do you think, maybe, the Betta could go in the 10 gallon if I even have a sick fish and need to take it out of the 10 gallon for treatment and put it in the 2.5? Because the only other thing I have is a fishbowl which I only use for transportation when we took my sister a Betta to her college.
Sand would be better, corys naturally feed by sifting through the substrate with their whiskers/barbels, with sand this passes under a special gill plate adaptation thing, but with gravel it is too large for corys to do this, so sand tends to be better if you want to see your cory feeding more naturally. Corys are also a lot less likely to get mouth infections like bacterial barbel rot if they feed off a soft sand substrate- gravel can be acceptable for corys if it is rounded and smooth, but if it is rough this can be quite damaging to corys mouths and puts them at a much higher risk of developing mouth infections etc.
So personally i would opt for a sand substrate- there are numerous types of sand you can use in aquariums, if you are a bit skint you can always use childrens playsand (which can look very nice and "natural" in tanks), but lfs (local fish store) will often also stock silica/blasting sand which also makes good aquarium sand, although this tends to be a bit more expensive than childrens playsand. Either way, always make sure you wash any sand you buy for your tank very thoroughly before you put it in your tank as when dry it is very dusty and if you don't wash it out beforehand under a hose or tap in a bucket, it will make your tank very cloudy looking. Never use building sand though as it contains all sorts of nasty stuff toxic to aquatic life like setting agents and stuff etc.
The 2.5gal tank is absolutely fine for the betta, however if it doesn't have any filtration you should do once daily 100% water changes on the tank as otherwise toxins like ammonia from the fishes waste will build up in the tank very quickly and put a strain on the fishes health.
You should read up on "cycling" tanks (also know as new tank syndrome) a.ka. the Nitrogen Cycle- this basic process is vital to learn about as it is the way the water quality works in aquariums, and understanding good and bad water quality and how to keep good water quality is vital to keeping healthy and happy fish

. The article in the link below is a good place to start to learn all the basic stuff about cycling tanks;
http
/www.fishforums.net/index.php?showtopic=10099

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