As I read your question, I see that you have two issues: (1) how you can become familiar with Linux without shifting to a complete new infrastructure in your home environment; and (2) what tools you can use that are common to both Windows and Linux, so you can leverage your work at home in the office.
To the first issue, there are a number of ways to get acquainted with Linux without having to install a separate Linux box. The quickest and easiest is to use a LiveCD, which is essentially a Linux distro that you put in your CD tray of your Windows box and it will run a Linux system from the CD. Knoppix is perhaps the best known of these and you can easily find it and download it.
Regarding the second issue, there are many open source products that run on both Windows and Linux. You can search SourceForge for the type of product you're interested in. Once you settle on one, there will typically be links for both Linux and Windows versions of the product.
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