Best banking would be visiting the bank vs online, however if she must use online banking, I cant suggest anything more secure or equally secure to that of what I already shared....However I hear that Norton Internet Security is pretty good at keeping problems away, and if your running that you would also be running Norton Antivirus. Norton is good, but is a resource hog, so i dont run Norton anymore and only my corporate clients use Norton these days. Norton Internet Security also comes bundled with many systems so she might already have it, but it might be out of date if not updated with a subscription to Norton.
If she is the only one using her computer and no one else uses it, she is probably low risk for problems, however if others are using her computer and downloading stuff on it and going to questionable sites then she is higher risk for problems.