That's a DIN and a half...you'll need to drill some new holes in the bracket to make it fit and something to cover up the gap.

What other solutions have you looked at?

Have you checked out the Scion head units?

 

I don't know if you'd like to save money but:

Pioneer DEH2200UB is amazing.

It's got USB support so I plug in a flashdrive, gets even better, I can organize the music on the flashdrive with folders! It's amazing.

Sounds awesome and very easy installation.

 

Pioneer headunits are just very nice in themselves. I had a Pioneer DEH-P3100 in my old Camry. Very nice unit.

 

if you plan to replace your stock unit, may as well go with something nice. I used to have Pioneer stereo on my other car, pretty good. But what you show seems to be pretty outdated (from the picture)

It is very easy to check, you can pull the plastic at the end of the shifter, then pull it out (from bottom, toward the front/top)
You will have access to the whole radio unit, just remove the 4 bolts.