How can I frame a mirror with trim?
The fastest/easiest way is to:

Mount the bottom trim to the wall making sure it's good and level. If you're going to use finish nails I would also run a bead of PL or similar construction adhesive first. If that's a little too permanent for your taste use trim head screws
Plum a line of the point of the miter up to the height of the top trim.
Tack a side piece on the line.
Set the top piece off of the reference point created by the miters with a few nails/screws, checking for level. Build a little leway into your rabbet so if you can keep your miters tight even if its a little off of plum and level.
Check the other side and if it looks good finish securing your top and side. If not you might have to tune your miters.
Once you've got everything fitted, slide the mirror into place from the open end.
Apply remaining trim piece.

The down side to this method is that it can be difficult the get your miters to line up if the wall doesn't form a nice flat plane.
A more involved method is to create the frame first off the wall and apply around a pre-hung mirror.

Attach a ledger to the wall at the height you want your mirror.
Apply a liberal amount of silicone to the back of your mirror.
With a friends help, set the mirror on the ledger and press into the wall.
Take a few scrap blocks and screw them off to the studs above the mirror. (See drawing) As you tighten the screws the block will pull the mirror tight to the wall and hold it in place while the silicone goes off.
Don't over tighten or you might crack your mirror. All of this can be accomplished by using the mirror brackets you mentioned but then you have to notch out around them which is a real pain.
While you wait for your silicone to dry, at least 24 hours, construct your frame.
Once your mirror is secured and your frame is dry, remove the ledger and blocking and apply the frame in whatever manner you're most comfortable with being careful not to hit the mirror with any fasteners.
This method is probably overkill for you (usually it's reserved for much larger mirrors) but it does give you the opportunity to really fine tune your miters.
As for expansion and contraction, it's not a concern. Wood moves very little longitudinally, only tangentially and radially.