Summary table of rolls needed to engineer each grade and totals to reach G4 and G5 on the right.
INARA is the most conservative of the big 3 but if you want to cover every base for your first time at an engineer, then go with the rep=0 numbers. Once reputation is established with a given engineer, the numbers should come down to the levels shown in the rep++++ row.
After you have gained access to (bribed) an engineer — and before you start building anything — there are often other ways to build rep with them, such as selling your exploration data. Check
|G1||G2||G3||G4||G5||G1 to G4||G1 to G5|