I believe the Griffin StudioConnect does not have a mic input, just a 1/4" guitar/bass, line in and MIDI.

For $150, you can get the iRig Pro which has an XLR connector for mic, a 1/4" for guitar/bass and a MIDI interface.

You can plug any xlr mic into it, they are inexpensive, widely available used on craigslist, and come in a huge range of types. The $100 Shure SM58 is well regarded. The Behringer XM8500 is ony $20, and will probably work great for you as well, so you can see the versatility in having a mic preamp and XLR connector like the iRig Pro provides.

It also has 30 pin, lightning and usb cables so you can hook it up to mac/pc/old ipad/new ipad. I have one and like the device, it's very compact and sounds good. I carry it and it's cables in a Tom Bihn Organizer Pouch

For $160 you can get the Presonus AudioBox iTwo which has a second xlr mic/1/4" input, allowing you to record acoustic or electric guitar and vocals simultaneously, for instance. It also comes with mac/windows software to edit your performances.

Then going on up they keep getting more expensive and have more features. I like having the mic preamp in the same device and the ability to hook it up to my mac or pc, so I spent the extra money on the iRig Pro. If I were doing it again today, I would probably buy the Presonus for the larger, sturdier box and the second input.

Have fun!