Macbooks come pre-installed with a very simple but powerful photo editing and storage program called iPhoto. It makes it very easy to download, organize, and edit photos.
The computer should be very fast and have substantial memory. A large hard drive for storage would be mandated. The software is a very important condideration for this activity.
In general, there are no specific computers to edit or organise photo's. It mostly depeds on the software installed on the pc. All new computers sold today are capable of editing and organizing photos. Be sure to install appropriate software!
If you are talking 10000+ photos you can throw as much power at it as you can afford. Harddrive arrays (RAID), lots of memory, solid state drives and a lot of processor power will each make a difference. Mac or PC is a matter of taste, preferred software and budget.
I find IrfanView to be the best program to manage and edit my pictures. It is very user friendly unlike photoshop. Of course it is not as complete but much easier and accessible.