The minimum to open an account is between 500 to 1000. It depends upon the bank or institution you are opening it up at. the max you can put in per year is 2000. But, depending on age you can do up to 5,000 in 'catch up' deposits. Unless you are in some kind of employer program that gives a match, it is not likely that you will have a minimum each month.
I opened a ROTH IRA with my credit union several years ago, I don't recall them having a minimum to open the account and I put in a two figure amount monthly. At the end of the year, if I have extra funds, I add accordingly as I can financially afford.