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).

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.