OP, you do obviously need to get stronger, but no you do not have to follow a “strength program” or do “starting strength” or listen to the advice of people who don’t even look like they lift weights, much less have the body you want to have.
My advice would be to read the Best of T-Nation sticky in the bodybuilding forum (threads by and about people that are actually big), especially the “Do This Routine Instead of That Dumb One” thread, and then either follow one of those or make your own routine out of a few basic freeweight exercises for each muscle group.
If you want my recommendation on a routine, it would be: chest&triceps, back&biceps, shoulders&traps, thighs&calves, rest, rest or repeat
Flat, incline, and flyes for chest; Lying and overhead extensions, and pushdowns for triceps. Pullups or pulldowns, barbell rows, T-bar rows for back. Barbell curls, concentration curls, and hammer curls for biceps. Seated DB or BB press, DB side raises, and DB rear raises for shoulders, barbell shrugs for traps. Back squats, stiff-leg deadlifts, leg extensions and leg curls for thighs, standing and seated calf raises for calves.
3-5 sets, 8-12 reps for the big stuff, 12-15 reps for the little stuff. Working up to one or two sets of non-stop reps to failure for each exercise in whichever rep range. Fighting to add reps or weight to the big stuff every session, the little stuff should be going up in weight at least every month.
That is honestly the routine I would do if I could fly back in time to when I was underweight and benching 155lbs. Just putting that out there.