Managing and sharing photos
Solution

You can use Apple iCloud's "My Photo Stream" to hold more than 10,000 photos.

You can easily continue to use iPhoto/Aperture/Photos.app so there's no need to learn any new app or to migrate data.

Upgrade Storage

The only limit is the total size of your photos and the storage you are paying for. 5 GB are free with every iCloud account.

See iCloud storage plans and pricing for more information on the pricing in your country.

Details

My Photo Stream does not limit the number of photos that you can upload. Keep in mind that Apple has a soft limit on how many photos you may upload per day:


  My Photo Stream upload limits
  
  The My Photo Stream limits below are based on anticipated upload
  patterns. These are the My Photo Stream upload limits:
  
  
  Uploads to My Photo Stream per hour: 1000 photos
  Uploads to My Photo Stream per day: 10,000 photos
  Uploads to My Photo Stream per month: 25,000 photos
  
  
  If
  you exceed one of these limits, your uploads to My Photo Stream will
  pause temporarily, and you might see a notification on your device.
  Your uploads will resume automatically when you no longer exceed the
  limit, such as in the following hour or on the following day.


Source: Apple