There are several systems of numbers in Japanese. If you want to count things, use the “hitotsu, futatsu, mitsu,…” system. However, there are more that get more specific for different kinds of things. They take into consideration if the thing is long and round like a pencil, whether it is thin and flat like paper, etc., but the “hitotsu, futatsu, mitsu,..” and the “ichi, ni, san, shi, go..” systems will just get you started, and the others are just renditions of them.
If you want to count money, use the “ichi, ni, son, shi, go,..” system. However, you will seldom need that small of numbers to count money. One thousand yen= sen 円 (en). Two thousand yen = ni sen 円 (en). Three thousand = san sen 円 (en), etc. One hundred yen= hyaku 円 (en). two hundered yen = Ni hyaku 円 (en). Three hundred yen = San biyaku 円etc. (Sometimes the pronunciation changes according to which letters come before it like in “san biyaku.”)
If you want to count people, use “hitori, futari,..” As you can see, it is kind of a branch off of “Hitosu, futasu, mitsu..”
If you want to count long round things, use the “ippon, nippon, sappon,…” system. A you can see, it is like the “ichi, ni, san, shi, go..” system.
I can’t remember all the sytems, but there are many. If you just learn the “ichi, ni, san, si, go..” and the “hitostu, futastu, mitsu, yotsu…,” they will get you started. Just remember that the “hitostu, futastu, mitsu….” counts things, and the “ichi, ni san, shi go..” counts money.
By the way, they also have “nana” and “yon.” “Nana” means “seven” if you are talking on the telephone, and “yon” means “four” if you are talking on the telephone. They use them because they say the other numbers are hard to understand on the telephone.