Lee dies work great so far as I can tell for pistol. Have never used their rifle dies. You will need appropriate shell plates for the LnL AP, and some more bushings will speed things along, but aren't necessary.
HF tumblers may be ok.
Calipers and a good scale are mandatory IMO.
For rifle you will need a way to trim, the Lee cutter and gauges with drill adapter work well enough, and are affordable, need a chamfer/deburr tool also, you can use this to remove primer crimps if need be.
I suggest getting the Lyman manual, I believe version 50 is out now, supplement this with powder manufacturer data, almost if not all have it available on-line it is not a substitute for a good manual though.
Get the press running proper first, then worry about the feeders, you'll know when you're ready for them. Mount that progressive solid on a heavy or anchored bench it will work much better. Go very easy on the adjustment pawls, it takes very little movement to make a substantial difference. Contrary to the manual, they will likely wear in and you will adjust them a few times in the first several hundred rounds and then not have to touch them again.