Choosing Between SQL Server 2008 R2 and SQL Server 2012 - Which to learn about first? As the title suggests, I'd like to get advice on which version should I learn about first?

Most online courses now emphasize on 2012 and Microsoft no longer gives out exams on SQL Server older than 2012.

My gut feeling says go with 2012 and study the hell out of it.
However I'm currently using SQL Server 2008 R2 at work and the company has no near future plans of upgrading to 2012 yet.

What should I do?
Yes, The certification exams for 2008 R2 are retired, but you can start learning 2008 R2 and once you master the concepts, move to the new 2012 features.

Even if your company (current) has no upgrade plans, your future company may already have upgraded all their servers to SQL Server 2012. 

Check out What's new in SQL Server 2012. Also check Top 5 SQL Server 2012 Features by Aaron Bertrand.