Best projection for an equatorial continent map?

[Hai-Etlik]

I'm mapping an equatorial continent on my fantasy world that's roughly the shape and position of North Africa, extending to about 35 degrees south. I have it in equidistant which is fine, but I wonder what projection would be best to show equal distance? Any suggestions?

Also any recommendations for what software to use to make projections?

Your description is bit hard to interpret. You say it's at the shape and position of north Africa, but then give a southernmost point close to that of the southernmost point in Africa as a whole. The best I can make of your description is as if the Gulf of Guinea, and a significant chunk of the eastern part of the South Atlantic had been filled in to make Africa rectangular? What makes a good projection for a continent tends to be a matter of the extremities, and of other technical requirements. A fantasy world may also lack the technical wherewithal for certain forms of projection. Chamberlin Trimetric is a very good projection for Africa, but it's quite advanced and can't be run backward easily.

No projection is completely distance preserving. "Equidistant" projections are only equidistant for measurement along lines running through particular points. Within a limited extent, a projection can be close to distance preserving for all distances, but the bigger the area, the less well it preserves distances.

You can plug Proj.4 strings directly into GDAL or QGIS to play with projections. It is not the most newbie friendly way of doing things. G.Projector lets you play with a bunch of generally fairly simple projections in a fairly easy way.

An azimuthal projection centred on the feature you're interested in is a fairly simple starting point. For shape with greater north-south extent than east-west, a transverse cylindrical projection might make sense.