Let me offer you this (for your arpeggios).
For major chords, the 3rd will always be
A) one string up (in pitch) and one fret down (in pitch) from your root
B) four frets up on the same string from your root
the 5th will always be
A) one string up (in pitch) and two frets down (in pitch) from your 3rd
B) three frets up on the same string from your 3rd
C) same fret, one string down (in pitch) from your root
For minor chords, the 3rd will always be
A) one string up (in pitch) and two frets down (in pitch) from your root
B) three frets up on the same string from your root
the 5th will always be
A) one string up (in pitch) and one fret down (in pitch) from your 3rd
B) four frets up on the same string from your 3rd
C) same fret, one string down (in pitch) from your root
here are some examples
Major (1-3-5)
G|--------------------------------------2----------------------4--7--
D|--------2--------------------------4------------4--7------5--------
A|-----4--------------4--7--------5------------5---------------------
E|--5--------------5-------------------------------------------------
(5-1-3)
G|---------------------4--
D|--------4---------5-----
A|-----5---------5--------
E|--5---------------------
(3-5-1)
G|-------------------2--
D|--------2-------2-----
A|-----2-------4--------
E|--4-------------------
Minor (1-b3-5)
G|----------------------------------2--------------------8--7--
D|--------2----------------------3----------8--7------5--------
A|-----3------------8--7------5----------5---------------------
E|--5------------5---------------------------------------------
(5-1-b3)
G|---------------------3--
D|--------3---------5-----
A|-----5---------5--------
E|--5---------------------
(b3-5-1)
G|-------------------4--
D|--------4-------4-----
A|-----4-------5--------
E|--5-------------------