I'm planning to get a bigger tank for my two fantails and I read somewhere (it may have been here or on another website, but I just can't seem to find it again!) that since goldfish like to search through gravel for food, it's best to get a fine grain type gravel, like sand, because larger pieces of gravel can get stuck in their throats and cause them to choke. Is this true or does gravel size matter?

The gravel I have now is a "typical" size. I've watched my fish sift through it and when they sometimes suck up a piece of it they always spit it out, but I don't want them to end up choking.

If you have a coarse sand, the goldfish will suck it up and squirt it out their gill plates. I had coarse white sand back when I was a kid, and they did that. This is fun for them but could abrade their gills over time. I later got regular gravel but the pieces were too small so the fish would pick them up and sometimes couldn't spit them out. So, it's best either to go with a coarse sand (really small rocks) or with gravel that's too big to get stuck in their mouths. As long as they can spit out the rocks they're picking up, it's fine. If you ever see one with a huge mouth, it may have a rock stuck in it. Normally, they can get it out themselves. Trying to intervene often causes more harm than good.

i had o clue they do that!! can beta fish do that also?

Bettas will pick stuff out of the gravel but I've not seen them pick up gravel. They're probably not as strong.