If your AV has access to an email scanner, all should be well on that front.. If not both the free version of Avast and AVG offer frontend Email protection.
As towards your primary question.. I myself forego a software firewall for a solitary hardware FW as I know what I'm doing, but this isn't your specific case; A software firewalls ability to monitor outgoing packets/traffic + email security might be helpful here. Layering both a hardware and a software firewall together affords the best possible protection, the only question: If the new owner can put up with the aforementioned hassle and nosiness of a software variant. I know I couldn't..
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