If Emsisoft Anti-Malware is working for you and do not wish to switch, renew your license, otherwise there is no harm in trying Norton Security - as it's being offered inclusive(?) of your Internet package.
In recent years, Norton Security / Antivirus has been very good in terms of performance, protection and user satisfaction (based on personal experience). To make sure I am clear, there is nothing wrong with staying with your current security vendor, or wanting to change, but Norton is a good option for security and peace of mind.
Other options that exist may take alternate approaches on security such as Application Whitelisting, Default Deny, Sandbox and Virtualisation, however, these can take time to learn and understand for full effectiveness. So my advise there would be to, if interested, test them on a spare machine and see if it works for you.
As always, it's good practice to keep a backup of your data and operating system for recovery.
For now think about what YOU want. Thanks for reading.