Python - 315 char

First time in codegolf! Only supports minor, major, diminished and augmented chords right now.

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);

Python3 - 315 char

First time in codegolf! Only supports minor, major, diminished and augmented chords right now.

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);

First time in codegolf! 315 characters. Only supports minor, major, diminished and augmented chords right now. It is in python:

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);

Python - 315 char

First time in codegolf! Only supports minor, major, diminished and augmented chords right now.

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);

First time in codegolf! This actually only supports minor, major, diminished and augmented chords right now. I'll add the bonuses after dinner. It is in python:

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);

First time in codegolf! 315 characters. Only supports minor, major, diminished and augmented chords right now. It is in python:

z=["C","C#","D","D#","E","F","F#","G","G#","A","A#","B"];y=[1,2,4,5,6]
def q(a):print(z[a%12])
a=input();k=(ord(a[0])+3)%7;j=k;m=4;s=0;f=7;
for i in y:
    if(k>=i):j+=1
if('#'in a):j+=1
if('b'in a):j-=1
if('m'in a or'0'in a):m=3
if('+'in a or"aug"in a):f=8
if('0'in a or"dim"in a):f=6;m=3
if('ma'in a):m=4
q(j);q(j+m);q(j+f);