How should I invest my part time job earnings?

A long term CD would pay better interest than a savings account. My advice - when you are mature enough to get a full time job, invest 20% of your pay to your 401K and choose mutual funds as investment on that 401K. Money you don't see, you don't touch. When you retire, you will have plenty to live on just by your own retirement money alone. Do not touch that 401K unless in a very dire emergency. Remember, 20% deducted from your paycheck that is saved is plenty when you retire. I did that and now living comfortably without relying on social security.

You could buy stock directly (no brokerage fees!) in a company that manages its own dividend reinvestment program. I have had such accounts with CenterPoint Energy (CNP) and Bob Evans Farms (BOBE), but the latter turned over its program to a company that manages such accounts for companies. I have an account directly with CNP and the dividends are reinvested in it (and I can add optional cash investments to my account to buy additional stock), but I also own the same stock through my brokerage account. My last brokerage statement showed that particular stock had an annual yield of 3.8%. You might prefer opening a brokerage account and having your dividends earned reinvested in the same stock. There are several companies whose annual dividend yield approaches or exceeds 4%. I'd recommend CNP, DOW, T, MO. (I'd caution you to avoid financials stocks, that is, large banking firms. Most of them are currently low performing.)

A Roth IRA would be excellent. Off with as big an initial funding as possible, then wholly fund them each 12 months (to the legal restrict), chiefly even as you are young. Two strong businesses to appear at: American funds; stay clear of and Cox.