Since it is a PRE-2013 model you already have the rear top panel (handle cover) that is needed. If you have the back rest you also already have the holes in that cover for the top case bracket. If you don't have the back rest then the location for those holes is marked on the bottom side of the cover with a cross hair mark.
In either case I would suggest the Suzuki official rear mounting plate for the 2013 models... which will fit perfectly on the earlier versions since the mounting spacer and bolt pattern is the same. The Suzuki plate is aluminum and is designed for the Givi or Kappa Monokey cases. It is also less cost than the Givi mounting brackets and plates since you would have to buy both a bracket and a plate whereas the Suzuki item is just the plate that does what both the bracket and plate from Givi does.
Then for a case I would suggest picking a Kappa Monokey case. Made by Givi but costing less for the same volume as the Givi cases. These can be bought for a really reasonable price if you don't mind ordering from overseas.
Rear plate and mounting hardware (get both items on this page):
2013 Suzuki AN650L3 Stopper Set Rear Box Plate (Optional) | CyclePartsNation Suzuki Parts Nation
Kappa K49N top case (47 Liters):
Kappa Top Box Monokey System K49
I go to the Kappamoto.com web site to see what model I would want.
Then I do a Google search for that Kappa top case and then select the Google Shopping link to see where it is the best price.
Using the above links I calculate the total price could come out to around $340-$350 shipped at the time of this post.
On my Burgman 650 I installed this setup but the top case was the Suzuki branded top case... which is the very same as the Kappa K49N case with the Suzuki logo on it. I bought from a member here a few years ago and posted about the install in a thread on this forum.
Installing the official Suzuki top case and mounting...
Another option I've used is to go with a Bestem top case but that would require you design and make your own bracket and mounting plate for the Bestem plate to bolt to. That cost would be slightly less after adding in supplies for the mounting and also would bring in a lot of extra work in addition to what is needed for the Suzuki/Kappa set up above.