You already suggested pyodbc, and I am going to agree with you.
It has given me the least amount of issues in my experience; I've used pymssql and adodbapi, and when those threw exceptions/created issues, I swapped out the code and replaced it with pyodbc and it either fixed the problem, or gave better error messages so I could debug faster.
It's worth mentioning that I primarily use it to connect to MSSQL Server DBs.