I kept my kids' money in a savings account until they were in middle school which was a mistake from my perspective. I always meant to invest it for them and I only wish I had invested their money sooner so it could have grown more than it has. I used UTMA accounts. I have never had any issues with buying or selling in any of their accounts. I used company sponsored DRIPs (dividend reinvestment plans) and stuck with plans that didn't charge investment fees on new investments or reinvestment of dividends. They did charge fees to sell and some for the initial setup. My kids had two stocks that would allow them to invest as little as $10 at a time. There was some trial and error on my part with some of my initial stock picks. I picked companies that had a history of paying an increasing dividend. Even with one of their stocks tanking and two only doing so so the others more than made up for it.

If I had to do it all over again I would probably use a regular brokerage UTMA account since most no longer charge buying and selling fees and I then wouldn't be limited to only certain stocks. I personally prefer individual stocks but you could make it simple and go with an ETF or an ETF that pays a dividend like SCHD.

You might check out Stockpile. They have a mixture of stocks and funds to choose from.

My oldest is in college and sells his stock to cover college expenses not covered by is scholarships.

You have lots of options: savings account, stocks, bonds, CDs, EFTs, mutal funds, CEFs. Just be sure to do your research for whatever investing path you decide works for you. The most important thing is that you save for your kid and invest in something. A lot of people mean to save/invest and life happens and they never get around to it. Good luck!