Can Bad Rotors Cause A Shimmy or Wobble?

I recently took a 95 Neon off of my wife's step-grandfather's hands. He's always done his own work, including brakes. The last time he changed front brake pads was about a year ago. I noticed that when driving the brakes squeak, but more noticeable, is the drive. It feels like a tire is out of round, or lopsided. The tire balance is OK and air pressure is good. I found out that when the front pads were changed the previous 2 times, that Grandpa didn't touch the rotors. I pulled the rims off and they're pretty worn and look to be worn a bit unevenly. Can these really bad rotors be a cause of the shaking and wobble? Obvious to me, they're the easiest to get at before looking closer at suspension and steering. Are the rotors the first obvious place to look?

I thank you in advance. Appreciate your help. By the way, this Neon seems like it's a blast to drive!

Neons are real sensitive to wheel balance and you will feel it at or around 60 MPH. They should be balanced with in 1/16th of an ounce as opposed to 1/8th.

Take the rotors in and have them turned if they are that bad and if they cannot be turned, replace them.

Thank you. I know Gramps put new tires on the front about 3 months ago. He's a Sam's Club guy so, with that, I'm not sure if their techs would know about balancing the tires to 1/16 oz. I'll check out the tire balance as you suggest. Also, I did pull the tires off the front and the rotors are pretty bad. My guess is that they'll need replacing.

Again, thank you! Unless there's something else to consider, I'll go this route: 1) Check tire balance, 2) Replace rotors and pads.

God Bless!

Sounds like a plan.