Accounting systems are either paper-based or computer-based and what is appropriate for one law firm may not be appropriate for another. However, it is best to choose and rely on one system, rather than a combination of systems. Using a combination of systems increases the likelihood of errors such as missed or incorrect inputs of information.
Most of you will purchase accounting software.
Whatever system you use, it must be capable of handling your office transactions. The difference between a paper-based system and a computerized system is a difference in process, not in requirements.