The minimum for some funds like the Target Retirement 2060 Fund, is $1000 for UTMA accounts.https://personal.vanguard.com/us/funds/snapshot?FundId=1691&FundIntExt=INTIf they don't have that much yet, you could keep a Mom's or Dad's ledger that shows how many shares they own in one of your accounts. You'll just have to add the right amount of reinvested shares each quarter when dividends are added. When it gets to $1k you could start their own accounts. Prepare them for the fact that their values could drop 50% occasionally, but it's OK and will grow in the long term.
We went the $1000 minimum route with Target Retirement 2055 in a UTMA for our kids. We saved up the Christmas and B-day money till they had $1000 then opened the account. I think you can open a brokerage account and do free trades of ETFs. Not sure if there is a minimum there, but you could potentially buy a single share of VTI or whatever for $100 or so.
Vanguard still seems to have a $1,000 minimum ("The minimum initial investment for a Vanguard UGMA/UTMA is generally the same as that for regular accounts, which is $3,000 in most cases ($1,000 for Vanguard Target Retirement Funds).").Schwab, however, will let you in for as little as $100: http://www.schwab.com/public/schwab/investing/accounts_products/accounts/college_savings/custodial_account.See also http://forum.mrmoneymustache.com/investor-alley/where-to-start-a-child%27s-roth-ira-with-very-low-income/.
I would caution against Schwab because this may be their primary account for the rest of their life, and Vanguard is going to save them a lot of money over the long run with the lower fees. Schwab has some low-cost funds, but they are always geared towards moving investors to their profit centers.
