You'll need a holding no. first if you don't have one, this tells the authorities you're keeping a farmed animal.
Then you'll need a herd no. for your pigs.
Finally moves are now electronic. In E&W you'll need to register with the e-aml2 system, in Scotland with Scot-eid
You'll also need to keep a movement register that must be updated within 36 hours of a move, and a medical records book to show what medicines (if any) have been given to your pigs.
South of the border, you do not need to specifically tell trading standrads, but as Robert says you should store your feed away from possible contamination such not bext to pesticides, and keep stored food rodent proof.
As a pig keeper ypu'll also come under a myriad of other rules and regulations, such as the Water Regulations 1999, governing how you connect your pig's water to the water system and notification therefof and if making a profit these can include silly things such as doing an annual ladder inspection report! However don't panic, everyone in every walk of life breaks a mass of minor regulations everyday without being aware of it, and if you are sensible then you should be ok.
On breed go for what you like the look of, everyone has their favorites.
As for general care - get a good book [advert warning] such as ours, or go on a course to get a real feel for how to set up and care for your pigs [advert warning off].
Pigs are really fun to keep, so enjoy your new venture