I have the Breach Lock Challenger kit, and it works. Mine came with both press mounted primer tools, and a complete hand help primer tool, and the required shell holders for the hand tool. The included deburring tool works, but it's not the best.
Both of those kits have the same press included, the only difference is the extras that come in the package, so worst case, you can always pick the other stuff up at a later date.
It looks like the Anniversary kit seems to come with their Ram Prime system instead of the hand primer, and I really didn't like that setup at all. I bought it after I had the Challenger kit, and it was much slower than the hand primer, and did not give me as good a result. I just didn't like the feel of it.
The breach collars are very nice to have. You can change dies with 1/3 of a turn, as opposed to the 20 or so turns normally required by the thread pitch. But, you don't HAVE to have extra collars. You can just leave the collar in, and unscrew the die from it like you would with a normal press.
On top of the Lee kit, you will need to buy a set of die for each caliber you want to reload, and a shell holder for each caliber also. That one bit me in the ass when I ordered a 9mm die set... I forgot to order the shell holder with it, so I ended up paying shipping twice.
For .223, I settled on a short base die set from RCBS since it had the least difficult setup, and the most sure fire way to get good sizing. Yes, it works the brass more than other dies, but it's simple for a beginning reloader to setup. Just turn it in until the die hits the shell holder, and start sizing.
You will also need a case trimmer of some sort. The Lee kit comes with the generic parts for their trimmer, but you will need to buy the rest of the trimmer for each caliber. Their trimmers are not the best, but they do work, so for just starting out, use it till you get sick of it, then research a new trimmer. I ended up with a Possum Hollow trimmer for .223, because it's much faster, and easier on the fingers than the Lee trimmer, but I still use a Lee trimmer for .243, and 30-30 since I don't load anywhere near as much of those as I do the .223.
I'd also suggest a decent electronic scale. The balance scale it comes with works, but it's slow, and tedious. I use my balance scale as a double check for my electronic scale now, with the electronic doing every 10th load, and the balance checking the first and last of a batch of 50 charges.
The case lube included with both kits will work, but I ended up using a spray lube, and getting better results, as well as it being much faster, and cleaner.
All in all, I like my Lee setup. I'm not thrilled with the carbon steel in a lot of places, so keep you handle oiled, and the Perfect powder measure can be finicky if the tension screw isn't set just right, but over all, I think they are a decent value.
In all fairness, I have never used anything but this Lee press, and their hand press, and I'm still pretty new to the reloading game, so take it for what it's worth. The Lee works for me, and I think it's a good way to get started on reloading.
Edit: A short list of other things I have bought that weren't included with my kit:
ABCs of Reloading: A good starter book with step by step instructions on how to do it, and why you are doing each step.
Lee Modern Reloading Handbook: Also a good starter book. There is a lot of generic load information in the back half of the book to get you started.
Electronic scale: Much faster, and easier to read than the balance scale.
Tumbler, media, and separator: A must have item if you want to reload mil surplus brass. Not as important if you are sizing clean brass, but still handy.
Swager Die Set: Also a must have if you want to reload mil brass.
Bullet Puller: I got the cheap kinetic hammer style, and it works, but it takes some work. No one is perfect, so you will need it eventually.
Calipers: A good set is pretty cheap, and they really are a "must have"
I can't stress this enough: Read both books cover to cover TWICE before you reload anything. Make sure you understand what you are doing. Once you have the basics down, always remember: Start with a LOW powder charge, and work your way up from there. Then go have fun.