The Anniversary kit is nice and will get you started. I also think it is a good way to start and learn how to reload. It also gives you everything you need without a large investment and allows you to determine what you are going to want in the future. The powder measure in the kit is a cheesy little thing but you will be using the autoprime and the scale for a LONG time. The press is also a serviceable unit and will load many thousands of rounds.
I am very much partial to Redding for single stage and Dillon for progressives, but to approximate the Lee kit in Redding equipment could be $500 easily. That is awfully steep to get your feet wet and find out if reloading is for you, especially when the Lee stuff works.
The Lee loader is a die/reloading kit. I used one years ago. The way I remember it you supply a hammer, bullet, powder and primer. You hammer the primer out with the decapping punch, size the case in the die by hammering it down on the case and punch it out. Then you punch the case down over the primer (this is the only step that made me nervous) and then fill it with the right amount of your powder and then use the hammer to tap the bullet seater down to the OAL you selected. IIRC it does not crimp the bullets into the cases but in almost all normal shooting it is OK.
Several distance shooting and benchrest records were held for a long time with the little Lee loaders, so you know they work. It was just a PITA to me to use. I would rather have a hand press to work up loads at the range.