I am relatively new to using Linux. I am looking to find a USB headset that I can use for both skype as well as use in Steam games. I am looking for ideas on which hardware to purchase, both usb dongle as well as it will be on a desktop.

Almost any USB Bluetooth adapter will work. The cheap Chinese adapters usually have a CSR chipset which is fully supported under Linux. As for the headset itself, they are all essentially the same so it doesn't matter.

As long as your BT adapter is supported and BlueZ is configured properly, any headset will work. Though you didn't mention if you wanted a stereo headset or not. Stereo BT is a little different than the standard headset profile, but you should still be able to get it working (and even if you couldn't, you can use a stereo headset in regular mono mode anyway).