those are retirement and extreme emergency funds.
dont feel bad about buying something fun. just make sure it isnt stupid and fun.
Another good choice might be investing in property for long-term renting.
Schwab is a solid broker that also has a pretty well regarded consumer bank.
Most brokers just dropped trading fees, so investing is almost free.
On another note, how "flexible" (not sure what the right terminology is) are these brokerage accounts? Is it like savings where you can withdraw when you want, or like a 401K where once the money goes in it's super hard to get it out?