avast detects quite some phishing malware.
Although, it won’t be bad if you have other tools (like AVG antispyware) in your computer too.
WebShield is a protection on-the-fly that scans http (Internet) traffic even before any file is saved in your computer.
Standard Shield is the resident (file) protection of avast.
avast is not a suite, it does not act as a firewall. Try Comodo, PCTools or ZoneAlarm firewalls.