Cloth diaper question

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So someone recently posted a question regarding cleaning of cloth diapers that made me remember my question about it. What all would I need to "get started" with cloth diapers? Like how many of each item would be recommended? I've heard that you need pants kind of like a swim diaper to go over the cloth diaper itself. Idk though. I feel silly asking but really am interested in trying this out. 
Does it actually save money? I plan to wash them at home myself rather than have a company pick them up and wash them for me. Unless, the cost of such a service isn't outrageous. 
And, I've heard not to use the cloth until the cord falls off since it can snag on the cloth and such. Is this true? 
I have a one year old already and she still has a ton of diapers that will fit for a while, but do they come in different sizes in case she isn't potty trained by the time the diapers run out? Would I use the same size cloth but different size pants or something as I would use for a newborn? 
Ugh. As you can tell, I am a complete newbie to this and I've read info online but I figured the best way to get answers would be to go to moms and dads who have done it before!
Thanks for reading and I appreciate any advice offered!! 
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