By default Picasa Web Albums give you 30GB of space to store your images, which is part of the Google Apps storage (Mail and Drive). Depending on the size of your images, that should be enough space to store hundreds of pictures.
To fit more images in your albums you can resize the images. If you make the pictures a smaller size, they will take up less of your storage space. You can use the “Creative Kit” option mentioned earlier to resize your pictures even after they have been uploaded to Picasa, thereby reclaiming some space.
Note: If you resize an image down to 800 pixels on its longest size (or smaller) then Picasa does not count that picture at all toward your storage limit. Technically you can store an unlimited amount of pictures as long as they are not bigger than 800 pixels on their longest side.