Thank you all for your thoughtful responses.
Some of you had noted the high miles. This is not my primary vehicle. Bought this as a "project car" but glad I can drive it while I get my hands dirty, too. So, yes it is an older car (with lots of miles) but I am having fun working on it. Spent the past 11 months in the hospital with cancer at 39 so now that I am out, I am glad to finally be able to live this little dream of playing part-time mechanic!
Now, a few more details:
1) Some of you suggested rotating all tires. Have done that, along with balancing etc... Didn't help.
2) One thing I've noticed is that the steering isn't "sharp". I guess that is expected for this many miles. Again, the lower control arms were just replaced. Should I change the upper and the steering rod, too? Could this be the reason behind the shaking? What other component should I change?
3) One strange thing I have noticed is that when in low speeds (less than a few miles per hour) I brake and hold to a full stop, the car shift slightly to the front right. I want to make sure I am clear: this is not an alignment issue, where braking leads to car pulling right or left. This is more like a body shift to the front right. Imagine what would happen if the front right wheel stopped harder and quicker than the one on the left...
This could be a sticky caliper but again, they assured me that there were no issues there.