Are either of those fences a property line? Some cities how "set backs" whereas you have to build coops so far from adjoining properties. There have been chicken owners that have had to move coops. Just thought I'd mention that.
Plan well for ventilation.
Minimum space requirements *normally* recommended...4-sq-ft of coop space per bird, 10-sq-ft of run space per bird. More space is *always* good...in situations where chickens have to be in the coop area for extended periods of time due to weather, etc., then more spacing is usually better.
Good choice on the elevated coop. That will retain the total footprint area for run space....16-sq-ft of coop works out to 4-sq-ft per bird and 48 sq ft of run works out to 4.8-sq-ft per chicken in the run. Plus, no sense in making a 4x4 coop walk-in as there would hardly be room to work and you should be able to reach most everything from a sizeable access door. Don't build it too short, though...build it tall enough for a roost and for space above the chickens head so that warm moisture laden air can gather and be vented outside well above their heads so that they are not sitting in a draft. Proper venting is very important, chickens create lots of moisture and you've gotta get it out of there!
As for not knowing how many chickens will fit in the coops shown in the coop section of the forum....go by the "rules" I listed above to figure out chicken capacity and you should be ok. I strongly urge you to look at the smaller coops to see how to arrange the roosts, nest boxes, feeders, waters, etc.. A 4x4 coop could get crowded with all of those items in it...and they can take away from the available sq-ft-per-chicken space.
According to the "rule" (and I say the word "rule" very loosely as folks get by with more or less space than that but it's a fair figure to strive for) you have a little bit of extra room in the run (for four chickens). If you move some of the equipment into the run you free up valuable coop space without encroaching to much on the chickens' run spacing.
Will the chickens be allowed to roam in the yard while you're outside working the garden? The reason I ask is that sunshine is good for them and if under a covered run all the time they will not get much. Maybe that area in front of the shed could be an extension of the run that isn't covered by a solid roof...maybe a 4x4 or 4x8 area? It looks like a sunny spot...that'd also give you more run area for them which is a win-win. ;)