Since you don't want to use the account to save for college, you can either setup a regular brokerage account for yourself and gift the money, or setup a UGMA/UTMA.
The brokerage account means you have full control of the money and the child has no claim on it, ever. Once you want to give money to the child, you can simply withdraw and gift it. You will have to keep the gift tax in mind. Assuming you are married, your spouse and you can each gift $15,000 (total $30,000). Any amount over that would reduce the lifetime exclusion.
UGMA/UTMA accounts are setup with the child as the beneficiary, and do include some small tax benefit. However, once you put the money in the account it is no longer yours, but the child's. They don't have access to it until the Age of Termination, which is 18 for UGMA and 18-25 for UTMA depending on the state you live in. You can technically withdraw money early from the account, but it has to be "for the benefit of the child". (e.g., you can pay for the family vacation, but just hope your child doesn't sue you for it once they're older...). Note that once the child does reach the Age of Termination, the assets become theirs and you no longer have any control over it. More reading here
Note that Vermont and South Carolina do not allow UTMA accounts (for whatever reason).
If you really are just saving money to give to the child in the future, a UGMA or UTMA account is probably what you want due to the small tax benefit. Since the money is technically the child's, it is mostly taxed at the child's rate. Here is some more info, including the tax benefits:
- Up to $1,050 in earnings is tax free
- The next $1,050 is taxed at the child's rate [often zero or at least much less than the parent's tax rate]
- Any earnings over $2,100 is taxed at the parent's rate.
Note that the tax is on earnings. Contributions to UTMA/UGMA accounts do not get any tax deduction.
Any of these three allows for the typical investment choices. Although, a UTMA account also allows other things like real estate, expensive art, etc.