Well, QGIS is not that good in creating of continuous rasters if that's what you want. Nevertheless it all depends on precision you wish to have in the end. If you wish to trade precision for swiftness - merge them all in GIMP and then georeference resulting image. But be aware that every modification of the raster increases the errors. So if you want to have more precision - georeference each image first, then crop them inside QGIS (Raster-> Extraction->Clipper) if you need. I would just try to make borders transparent in layer properties if it is possible. There is actually no need in merging georeferenced images - if you need to treat them as one you may just create a virtual raster (Raster->Miscellaneous->Build Virtual raster).
Best Answer
The raster you want to georeference most probably uses the
EPSG:2163
, USA National Atlas CRS.You should set this as your project CRS and target projection.
And also use
Thin Plate Spline
transformation method, with a significant number of reference points:This is the result of a first attempt, you should be able to reach a pretty good result with additional points: