I'd also recommend you read Joe Haldeman's The Forever War, which is very much a response to Starship Troopers: while Heinlein was writing from the perspective of WW2, Haldeman was writing from the perspective of Vietnam, and it shows.
Haldeman has said on many occasions (like nearly every interview with him) that The Forever War was absolutely not a response to Starship Troopers. He oughtta know, right?
I strongly support the recommendation to read both of them, though.
I haven't read Armor. I should check it out.