Is it more secure to run linux as a second operating system for this purpose?
It is always more secure to run Linux then Windows. You should definitely upgrade to Linux as soon as you can. You can use a Virtual Machine if you really need some windows program, but you have open source alternatives for almost all software.
As I have been advised to use a virtual machine: If my local computer is affected by some type of virus, wouldn't the virtual machine also be vulnerable?
Achow101 gave a great response to almost all your questions, but I think he misunderstood what you asked here. You asked if infection of your local (I assume you mean, what is called a host) system would leave a virtual machine that is running on the system vulnerable. The answer is yes, absolutely. The protection from a Virtual Machine goes the other way around. If the VM is infected, your host could still be secure, if the VM software doesn't not contain any vulnerabilities.