The information you provided is not enough to recommend anything specific.
Security model is usually based on trust relationships between servers and clients. If all clients are run in secure environment, then you can use root with all permissions to connect to the sever. Otherwise, you have to adjust your security policy according to (as I have already mentioned) your trust relationships model. By secure environment I mean that your scripts can NOT be modified without appropriate permissions granted to trusted people only, and your network is not vulnerable. For example, your scripts should not be on computers that also have http (with some buggy, free CMS), ftp and rdp services open to the Internet. This is the technical side.
Now the business side. You probably have a certain domain model that your clients operate on. Your scripts probably have roles (say sales staff, administration staff, etc). You probably don't want sales staff to be able to access administration tables, or whatever. This rises a security question. You can implement your security tier in 2 places: mysql server, rich client. You said that you run scripts (which are not rich clients), so your only option is mysql server. You might want to setup accounts and set minimalistic permissions on them. By minimalistic permissions I mean that each user is allowed to do only and only, what he needs to able to do.
Once again, you got to provide more specific information to get more specific advices.
See here for MySQL-specific security guidelines.