I have a view which is only accessible to authenticated users. However, there are links to it on the site. Can I make it so that an unauthenticated user gets redirected to the login page, instead of the 403 they're seeing now?
The Redirect 403 to User Login module should do what you need.
I would use Rules, it is very configurable and should allow you to do what you require.
With LoginToboggan, the login form can be added to Access Denied (403) pages. No redirects needed.