[V]

My GTA runs and drives, and that's kinda all I can really say about it right now, lol. The car previously sat 7-8 years. The handling and braking does not instill much confidence. So over the fall/winter I want to correct that.
**Only new parts installed so far are rear shocks(AC Delco) and front/rear sway bar end links(AC Delco).**

Upon initial heavy braking, the car seems to want to go left and right randomly. It doesn't always seem to pull in the same direction every time.
It'll seem to wander left and right and I'll have to correct with steering.
From what I could tell, no caliper is sticking. There is no excessive heat build up on any rotor/wheel while/after driving.
I plan on starting by just replacing all the rubber brakes lines. I had a pulling issue in my old 88 GTA and it was one line which would swell causing it to pull. After that, I'm thinking just installing new calipers. However, before I do calipers, I would want to make sure the issue isnt more steering related than brakes.

The steering is very vague. I have a lot of play while driving down the road. When going in a straight line, I can turn the steering wheel 45-60 degrees(like 5-6 inches) with no reaction from the car. Steering column/steering wheel itself is tight and seems not to be the issue. It would therefore lie between the rag joint, steering box, and linkage to wheels. Can the steering box loosen up that much? Or should I focus more on the tie rods and pivots for the steering linkage? I looked at all the ball joints and even though they weren't new, they weren't loose(by hand). Should I also consider the lower control arm bushings as a possible cause? I looked at them and they seemed intact. I really need a second person to help me diagnose the steering since I can't turn the wheel and be under the car at the same time so see what has slack in it. That's why I'm asking for help narrowing it down. Maybe I'll set up a camera or something next time I have a chance to look at the car.