Lone Star pays average CD rates for most terms, but the rates are lower than what you'll earn with many of the best online banks. If you want a term shorter than six months or longer than five years, you'll have to consider another bank.

You might like the Lone Star Bank Personal Savings Account if you can keep a $300 balance, because then you'll waive the $5 monthly service fee. TheLone Star Bank Personal Savings Account pays 0.50% APY, which is decent savings rate. However, if you want to snag a high APY, you can get a better interest rate with one of the best high-yield savings accounts.

The Lone Star Bank Smart Choice Checking Account is a solid option if you want an account with a low minimum opening deposit. It also offers unique perks, like roadside assistance and up to $10,000 in accidental death insurance. The checking account has a $6 monthly service fee that can't be waived, though. You can also choose from two other checking accounts, including one that will pay you tier-based interest rates on your balance, but keep in mind these accounts have higher monthly service fees (unless you qualify to waive them).