Danza,
You pretty much have everything you need, get some sterilizing powder (though you can use bleach if you rinse it very well. I use VWP sterilizer and never had any bad batches because of bugs. You can use the sterilizer for baby's bottles too. Making sure everything is clean and germ free is really the most important bit of homebrewing as a few bugs could easily spoil your brew.
The king keg can be used to carbonate, you just buy the C02 pellets and add them in. I don't keg though so best getting advice from someone else.
It'll keep fine, for a period of time. As long as you don't leave it in there for too long it's ok. But the plastic is all food grade and doesn't leak into the beer. Your fermenting bin will be plastic too (I assume) and that should be food grade plastic also, if you just bought a bucket from B&Q have a check. I bottle in glass bottles, and carbonate it through secondary fermentation (adding a sugar solution to the bottle before filling) though I would keg if I had the money and my brewpartner was happy with it. I don't think he's happy with the idea of me having a keg of beer in my fridge!
As for kits, that all depends on how serious you want to take it all. If you just want ease and quickness just get something like this:
http://www.innhousebrewery.co.uk/index.php?ecom_siteid=176&product_id=36183&option=Prod_detail
That comes in a tin, it's very syrupy and you just add that to boiling water (usually a gallon) and dissolve it and then top up bin with water. It also comes with the yeast. Only extra thing you need to buy is sugar. It'll tell you on the can how much sugar for each batch but you can use as little (if you want low alcohol) or lots (if you want a high alcoholic brew). Sugar is a personal preference, I've used lots of different types and haven't found any difference in taste.
You can add hops or anything else to that kit to edit the taste, aceface added some raspberry juice to one of his brews which he said worked well. Just trial and error really.
Another kit, which is more expensive but may make better beer (I've never used Milestone so not too sure) is -
http://www.innhousebrewery.co.uk/index.php?ecom_siteid=176&product_id=444884&option=Prod_detail