From what I can gather, as a baseline I would assume no one competent has worked on this Jeep. You need to go over everything with a critical eye. You could go back to the shop you initially took it to and complain, but I doubt you will get your money back, and I would not be inclined to attempt to trust them a second time.
Figure you need to align it, but before you do that you need to assure yourself you have good joints everywhere there is motion. Pay special attention to the track bar--those are notorious for causing problems. Kevin's Offroad is worth your consideration for the axle side. Make sure you have a quality, good condition joint on the body side. Remove each end to be sure of its condition.
As was mentioned, look at the mounting of the steering box. The factory spacer is a die cast aluminum piece which is prone to cracking. You want a steel spacer in there. A steering box brace is a nice addition, but I would be inclined to get everything you currently have under control before adding the brace.
Regarding the popping noise, I would be inclined to pull the front driveshaft right away just to make sure you are not losing the centering ball. If the centering ball goes it will probably take the transfer case with it. Very sub-optimal. Take the front driveshaft out and check all the joints. While it is out, take the Jeep for a drive and see if that makes any difference, even if the joints feel good. It is an easy test and costs nothing but the time.
After the driveshaft test I would confirm you have a good spacer behind the steering box.
Then I would check all the steering joints (need two people--one to move the steering wheel, other to feel each joint as the steering goes back and forth).
Then I would pull each end of the track bar and check those joints (If it were me I would plan to replace the axle end with an oversized Kevin's Offroad bushing/bolt).
Then I would check the joints at the end of each control arm.
Then ball joints.
If the popping source had not yet been found I would pull the axles and check those U-joints.
After doing all that I would put on good tires and align it.
That done it should no longer be darting while driving, but you probably will not have changed the ride quality. But I would do those things first, just to make sure that you can get it to behave in the steering department, before modifying things any farther. Get it to behave, then decide if you want to go with drop brackets or long arms. And then pick a shock absorber. Or even consider going for a high pinion D30.
Thinking of the axle, have you opened the diff and changed the oil? I would not regard it as a likely suspect for the popping noise, but if that maintenance has not been done I would confirm that the gears are fine in there. I would expect plenty of other noise if not, but if the tires and stereo are loud enough who knows what all might be going on.