As Varadarajan does note, complex reductive groups (implicitly, with forgetful functor from C-groups to R-groups applied) have a vastly simpler spectral theory, already treated by Gelfand-et-al in the late 1940s. Apart from Gelfand's old papers, which I cannot read because (sadly) I do not read Russian, I think Varadarajan's book comes the closest in the contemporary "book" literature to explaining the vastly simpler case of complex (semi-simple) Lie groups. (Although some of Gelfand-et-alia's papers were translated, they have many very-specific internal references to other untranslated papers). Given Serge Lang's interest in simplicities, I was a bit disappointed that Lang-Jorgensen's books and memoirs on related matters do not give a separate treatment of the complex case, apart from a few comments that the recursion in the general case terminates in the complex case.
It is true that in that book Varadarajan's writing style is unusually (and, to me, pleasantly) "organic", which seems to create a difficulty for some readers. Nevertheless, if V's book is too difficult, I would wager that Knapp's or Wallach's books (while excellent!) would be nearly impossible, in regard to SL(n,R) or SL(n,C) for n>2.
One reason for this is that, especially in Knapp, the main overall goal is to set up Langlands' classification. This is in a different direction from Plancherel.