Getting this right really depends on thinking it out before you draw anything. If you don't know what the projection is, you really don't have any idea where, what shape, or even what size the things that you are drawing are. You can change the projection afterwards, but if you got it wrong in the first place, this will just make it much more obvious. For instance, the polar maps I posted.
It took me a while to figure out what you meant by a "thread that has [projections] for download" but I'm guessing you meant this? http://www.cartographersguild.com/ma...raticules.html
Those aren't "projections". A projection is a method for flattening the globe onto a flat map. What Gilgamec has provided are graticules (Fancy map speak for "grids") of latitude-longitude (There are other coordinate systems that can be represented with graticules but you probably won't be concerned with them) which have been flattened using a number of different projections. They are the product of projections, not projections in and of themselves. Think of the expression "2+x". If you plug in "x=2", then you get "4". The projection is like "2+x", and what's in that thread is the "4".
They make good templates, but simply dropping one on top of an arbitrary map isn't going to work. The features of the maps (coastline, rivers, etc) have to be drawn in that projection. It's not something you can 'add in' later. At least not for a whole globe. For smaller areas, you can, at least sometimes, get away with drawing something without thinking about projections, and then add a graticule afterwards.
The reprojections of your map I posted were done using a program called G.Projector which is freely available from NASA. It can take maps in normal equidistant cylindrical projections and reproject to a wide range of other projections. It can also add a graticule and some simple vector overlays (like the Earth coastline I added) http://www.giss.nasa.gov/tools/gprojector/