Orthographic isn't usually a good projection for reference maps (It is good for "locator" type maps like the country maps in Wikipedia). It's essentially a view of the planet from deep space. So so toward the edges of the map everything is "foreshortened" making it squashed looking. You mention wanting to measure distance. I'm afraid you aren't going to make a map covering an entire hemisphere where you can measure distances to scale.
If you want a reference map of a hemisphere, I'd recommend the stereographic projection. It keeps shapes looking nice and recognizable, but distorts their sizes. In this way it's similar to Mercator (They are both "conformal") but it is centred on a point and has maximum (infinite) distortion at the antipodal point (the opposite side of the globe) where Mercator is "centred" on the equator, with infinite distortion at both poles. Those maps that have the two hemispheres side by side are generally done using stereographic projections centred at antipodal points on the equator.
Which projections are best for a continent depends on the details of the shape of the continent and a degree of judgement about which properties and which parts are important. My go to projections for reference maps of continents are Lambert Conformal Conic, Stereographic, and sometime Transverse Mercator. In general, LCC tends to be good in high latitudes, particularly if the extent runs longest east-west. Transverse Mercator is good for extents that are more north-south. Stereographic is good for more compact shapes.
North America:
LCC:Stereo:
Western North America:
LCC:Stereo:
Equirectangular is useful as something to feed into simple software like G.Projector. It's also useful if you want to wrap it around a 3d sphere in a 3D graphic program. It is not a good choice for finished maps though.
Mercator is designed for marine navigation, and it's also useful for zoomable maps on the web. Historically it has been used for reference maps of the world, although it is poorly suited to this and has largely been replaced by modern projections like Robinson and Winkel Tripel.
I'm afraid I'm not too familiar with any of the software you are using. As I understand it, Fractal Terrains has some limited capability for projections, and the rest (CC, Photoshop, and Illustrator) only work in euclidean geometry. Photoshop should have some filters that can pull off what are effectively come very simple projection transformations (Between normal equidistant cylindrical and polar equidistant azimuthal) under different names.
You'll probably want to either, do all your design of the world in Fractal Terrains (I don't know how much this is practical) and then export to your finished projection, or export to an equirectangular/equidistant cylindrical image, edit that in Photoshop to add/edit the features (don't worry about making it pretty at this point) then use G.Projector to convert to your final projection, and pretty up the resulting image.
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