Personally, when I do sets its just base and inserts NO parallels... Parallels are hard especially say 10/11 Donruss where they was 5 parallels (Base, Emerald, Sapphire, Ruby & Press Proof) Which, if collecting parallels blew the Donruss set out to 3000 cards.
if theres a parallel set i'll focus on that and forget the base. if there are multiple tiers of parallels i'll go for the rarest one and forget about the rest.
I completed the 96/97 Flair Row 2, 1 and 0 sets but no way would I try to go for the legacies also and then and only then call it complete.
I've been going (very slowly) with the 03/04 Bowman Chrome Golds /50 but have never thought once about adding the base set, I would however consider going for the standard refractors /300 because they are just nice also
I don't throw them away, nor do i really collect them but i definitely don't mix them in with base as parallels are a seperate card all together. About the only parallel sets I'm considering going for (when finances are healthier) are 1994-95 SP and SP championship die-cuts NBA and 2009 Score Glossy NFL as I already have a good majority of those sets as is.
Do you mean a set of any given base cards and its parallel(s), or a set of "base" version of any given insert cards and its parallels?
If it is the former, I would collect parallels only (if with multiple tiers of parallels, I would collect the one that is within my budget). If it is the latter, I would mainly collect the "base" version only - the parallels would probably be too expensive for me to complete in most of these cases.