If you want to display a country or region on or near the Equator, use a Cylindrical.

If you want to display a country or region in the temporate zones use a Conic.

If you wish to display a country or region near the poles use an Azimuthal.

If you want to display a country or region with minimal distortion for the map projection you chose,
change the map's ASPECT so that the area of interest is positioned at the center of the map.

If you wish to construct a world statistical map, choose an Equal-area Pseudocylindrical.

If you want to produce a world map that others can lift right off the web page and use in a gis program
choose the Plate Carrée (a couple of other names of it are the equirectangular and unprojected).


While most schools teach 4 basic properties of a map projection, here is a comprehensive listing
of properties to ponder preserving when constructing a map.

=============================
Graticule Groups
(or Fundamental Properties)
=============================
Azimuthal (or Planar)
* Perspective
* Non-perspective

Orthoapsidal
Pseudoazimuthal
Retroazimuthal

Conic
Polyconic
Pseudoconic

Cylindrical
Polycylindrical
Pseudocylindrical

Composit
Projections that are composed of two or more different map projections.

=======================
Representation Groups
(or Special Properties)
=======================
1) Conformal

2) Equal-area (also Equivalent, or Authalic)

3) Neither Conformal nor Equal-area (also Arbitrary, or Aphylactic)
Consists of any of the following:

3a) Equidistant projections

3b) Approximately Equidistant projections
The Meridional particular scale is a constant value but it's not equal to
the principal scale

3c) Abstandsgleich (German term, no English Equivalent)
Has Equidistantly spaced parallels and variable meridional particular
scales.

3d) Abweitungstreu (German term, no English Equivalent)
The particular scale along the parallels is equal to the principle scale.

3e) Absolute Minimum Error projections
Sums of the squares of the errors in the particular scales, integrated
throughout the area mapped, have a minimum value.

3f) Minimum Error projections
Has one or more of the Special Properties but satisfies the secondary
condition that the sum of the squares of the errors in the particular
scale have a minimum value.

3g) Périgonale (French -- No English Equivalent)
The maximum values of Angular Deformation are reduced to a minimum value.

3h) Périhalique (French term -- No English Equivalent)
The maximum values of Area Distortion are reduced to a minimum value.

3i) Périmecoïque (French term -- No English Equivalent)
The maximum values of Linear Distortion are reduced to a minimum value.

3j) Projections that are 'Total Area True' (flächengleich or atractozonique)
and also satisfy some property other than equivalence.

3h) Orthodromic
Projections on which great circle arcs are rectilinear.

3i) Loxodromic
Projections on which rhumb lines are rectilinear.

========
Aspect
========
Normal (or Direct)

First Transverse

Second Transverse

Simple Oblique

Transverse-Oblique

Skew

Plagal

============
References
============
Wray, Thomas, 1974, The Seven Aspects of a General Map Projection,
Cartographica Monograph No. 11

Maling, D. H., 1968, The Terminology of Map Projections: International
Yearbook of Cartography, v. 8, p. 11-65

Lee, L. P., Jan 1944, The Nomenclature and Classification of Map
projections,
Empire Survey Review No. 51, Vol. VII, P. 190-200

============
Paul B. Anderson FCCS (USN, Retired)
Kingsport, TN native living in Norfolk, VA

My Map Projection Graphics:
http://www.galleryofmapprojections.com/