i don't know anything about pugh, but I don't think rudin is the best book for self studying.
strichartz's the way of analysis isn't the best reference book but it describes things in a "story-like" manner which might help for someone self studying. ross's elementary analsyis is kinda comparable to a spivak calculus type deal, but more geared towarfds lower end analsyis.
ive also heard great things about rosenlicht's intro to analysis (its a cheap dover)