I've reloaded shotgun shells for a lot of years. My reloader is a HydraMEC 650 which I don't think is available any more but I can do 500 rounds in a little over an hour with it.
The Lee loader you pointed to will reload shells but if you want a better quality product I have to agree that the MEC 600 Jr is the way to go. I was reloading 12 gauge mostly for trap shooting and 20 gauge mostly for hunting. I used a 600 Jr for the 20 gauge stuff. The reloads are high quality.
All of the powder manufacturers have free hand books for reloading. For 12 gauge I liked Red Dot which is a bit dirtier than some other powders. A good way to get started is to shoot Winchester AA's and then reload with AA wads, AA powder and Winchester 209 primers. There are less expensive generic wads out there that work just as well.
My advice is to get yourself to a trap, skeet or sporting clays facility and start asking a few questions. You can get some good advice from the shooters there and can probably save some money on components. Most clubs buy in bulk and pass the savings on to their members.
Shotshells are very easy to reload since the powders meter easily so you don't have to weigh every charge. The Mec reloaders have charge bars that are made to throw the right amount of shot and powder every time.
You can also find shotshell reloading data on line. Just do a search and find the powder makers website.