I work in Virgina but live in MD but accidentally withhold income tax for Virginia instead of Maryland. Which TurboTax service will suit me best?

Your state issue doesn't so much affect the version of TurboTax you use as it does how many states you will need to file.  Your income types and return complexity is what determines which version you would use.  The free version only allows you to file one state, so you would need to at least choose Deluxe. 

The best thing to do is to start in Deluxe, then answer the beginning interview questions and TurboTax will then tell you which version you need to use. 

You will need to file 2 states. You will file VA as $0 income just to get a refund of your taxes withheld for VA.  Then you will file your MD return, claiming all the income you received. Since MD and VA have reciprocity, you will only need to pay taxes to MD.