I find most log-in page irritable, especially when I'm accessing the page from a mobile device. The real estate gets clogged by multiple options. A drop-down is an option, but I would advise against it as it's seldom used in login pages. You could consider icon buttons instead, following a default option with a button like in the examples I've listed below.
The objective of a login page is to allow the user to authenticate them into the application. The method / order of login service is irrelevant as long as it's a relevant way to get the user into the application. i.e. No one would use their LinkedIn account to log into a Pornography site; that's common sense anyway... and this common sense could help you determine which service/option is the default and other stacking details.
Here are some examples that I've liked. I'm using both mobile and desktop screenshots here. As you would notice, the real estate spent to provide login options is very little across devices. I also found this post which may be helpful to you.
and Best Desktop login (with too many options): StackExchange!