This dude has the right idea! While I doubt this works as well as an actual Worm Factory (short, stacking trays), it’s still a great start to see what you think of vermicomposting.
This is more or less the same process as building your own worm bin from a Rubbermaid tub. If you use 2 tubs (the bottom tub is for collecting leachate), it will basically function in the same manner as this.
In my experience, worms do better in a shallow environment, so a short Rubbermaid tub would most likely outperform a bucket… however, whichever you can get your hands on is the best for you. Go to any grocery store and ask for some food grade plastic buckets (food grade means the plastic doesn’t leach into the contents…or so they say)…they toss these out all the time so you’ll be doing them a favor. Further, get some extra ones just because! Buckets are awesome. And so is DIY vermicomposting!