You should not need to cache the image data if you are using Image Server. You can create raster mosaic datasets of the data and publish these as image services in ArcGIS Server.
As Michael mentions there is no real need to Cache such imagery. Caching them (or converting to prerectified tiles) actually has a number of disadvantages as it results in the imagery being flattened out and information in the overlap of the imagery is lost. The key aspect that affects storage is the scanning of the original imagery. Typically historical images are BW and scanned at resolutions of about 25um (1000dpi) on photogrammetric scanners or 40um (600dpi) for lower grade flat be scanners. Aerial Images are typically about 25x25cm. We recommend to use TIF with JPEG compression Q80 for such images. Including pyramids, the typical file size for such scans is about 12MB for 40um and 30MB for 25um. If using color imagery then use JPEG_YCBCR compression and the typical files sizes are 20MB and 50MB respectively. For some additional recommendations see the Image Management Guidebook that can be accessed through Image Management Section of the Imagery Source Center The recommended approach is to georeference the images, either using the georefercing tools in ArcGIS, else using orientation data if available and the same workflows for aerial imagery. There are many different ways to do this and the optimum depends on the number of images and accuracy required. In all cases the output should be a mosaic dataset that references the original images and defines the georeferencing and any clipping of the images. The mosaic dataset should also include the available metadata about the images so that when served as an image service users can access metadata and also control the overlap of the imagery to gain full information content. Over time as better georeferencing becomes available the mosaic dataset can just be updated. If you wanted to cache the data then this is possible. It can be done directly in ArcGIS for Desktop (see Manage Tile Cache Tool in ArcGIS 10.2) or Server. The resulting cache can be served through ArcGIS sever as a map service or packaged and uploaded and published through ArcGIS Online. Using ArcGIS Online is a very inexpensive way of serving the imagery as only low storage costs are charged.
The size of the cache can be computed roughly as follows: Cache Size in Bytes is approx (Width of Extents * Height of Extents / (pixelsize^2)) / 4 Or Cache Size in MBytes is approx (Km2/pixelsize^2)/4 in MB
The actual size will be dependent on compression, but this will give a rough indication. Typically what I would recommend is to do both. Serve the image service for users that want the full information content and create a cache more as a background map for general reference that can be made more widely accessible
