garage storage area project
ledger boards (is that the right word?)


That is the correct word


  Is 2x8 enough for this or should I use 2x10


2x8 @ 16" oc in the long direction of 14' will support more than 40 psf loading


  Which way should the joists go? (across the short or the long dimension)


The short direction is typical as it allows for higher loading for a given joist size or conversely a smaller joist for a given load. Blocking at mid-span of the joist is necessary. In your case, to avoid a beam, which would likely be deeper than the joists and undesirable in this case, I suggest spanning the longer direction.