Just to give a little illustration of what everyone else is talking about, here are the triads (without sevenths) with chord symbols in relation to C major:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Key|Signature:C
|Text|Text:"Gm v"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:-2,b0,2
|Text|Text:"G° v°"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:-2,0,b2
|Bar
|Rest|Dur:Half
|Bar
|Text|Text:"Dm ii"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:-5,-3,-1
|Text|Text:"Em iii"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:-4,-2,0
|Text|Text:"Am vii"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:-1,1,3
|Text|Text:"B° vii°"|Font:StaffLyric|Pos:-10
|Chord|Dur:Half|Pos:0,2,4
!NoteWorthyComposerClip-End
And about diminished chords such as B-D-F: they contain a diminished fifth (B-F), which causes a lot of tension. In tonal harmony, the tritone must be resolved (the diminished fifth should resolve inward to a third, we're not concerned about augmented 4ths right now), such as:
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Key|Signature:C
|Chord|Dur:Half|Pos:0,4
|Chord|Dur:Half|Pos:1,3
!NoteWorthyComposerClip-End
or
!NoteWorthyComposerClip(2.0,Single)
|Clef|Type:Treble
|Key|Signature:C
|Chord|Dur:Half|Pos:0,4
|Chord|Dur:Half|Pos:1,b3
!NoteWorthyComposerClip-End
And to add to what others have said, nobody has addressed the possibility of shifting into the relative or parallel minor. If you decide to do this somehow, in a minor key, i and iv are minor chords, ii, is diminished, and VI is major. 3, 5, and 7 depend on the type of minor mode you are using. If you are using natural minor, III is major, v is minor, and VII is major. If you are using harmonic minor (raised 7th), then III is augmented, V is major, and VII is diminished. You would probably want to stay with i, iv, and ii.