Amiga OS is not a secure operating system--no memory protection, no access control, etc.--so it's really up to you to determine what's safe to execute and what's not. (Actually, it's always up to you, regardless of the operating system.) I'd say the risk of a remote attack is almost nil, but using a simple firewall and address translation--features provided by most consumer routers--should mitigate any risk.
And it's probably a good idea to stay away random collections of games. There's a good chance they're pooh. Others on the forum can point out the best antivirus solutions for the Amiga.
I don't use my Amigas for online entertainment, so I don't have anything to recommend re: software.
