You will need:
BASICS:
ceramic, heavy food bowl (two preferably if you're getting boys, but one will do)
Cage - if you think it's a big cage go bigger for happy, healthier piggies. DO NOT get a plastic goldfish bowl cage; get one with bars. I hate pet store cages and fangirl over C&C cages (see: guineapigcages.com for what mean) but Nero 4's seem to be a pretty cushy cage and look great size-wise for two girlie pigs. If you're getting two boys, be prepared to need to make the cage bigger.
Hay rack (for lots of hay, unless you're using it as a bedding then you won't need this; careful of the hay rack, some are big enough for piggie heads to get stuck in

)
Water bottles (I always have one with one spare since I have a habit of breaking them by dropping)
Food (Burgess Supa Excel is one of the best brands you can get in the UK, above that is Oxbow Cavy Cusine (TIMOTHY based pelle) but it costs a lot, so Burgess is just as good. Pets at Home pellets are OK, but if you compare the ingredients list to that of Burgess you'll probably want to wallop P@H with a mallet)
Hay - I left this one to last because it's something which is very important in a piggies diet. I would *strongly* recommend that you don't get your hay from P@H because hay should make up 80% of your pigs diet, so, in my opinion, a good hay should be selected. I use thehayexperts.co.uk for my hay and I buy Oxbow Orchard Grass and Pure Pastures Meadow Hay (in bulk). Orchard Grass is a grass hay which is less dusty than Timothy Hay which is the recommended hay for guinea pigs. Orchard grass costs about £4 - £6 per 1kg, buy in bulk for less cost per kg, you will use it. I mix the Orchard grass with the lower-grade meadow hay and feed the mixture as the daily diet to the piggies.
All of the hay that I've ever gotten from P@H has been brown, dry and doesn't smell as nice as that you can buy from The Hay Experts; do not buy the Timothy Hay from P@H because it's tough and every batch I've ever gotten has smelt old and musty. I didn't even notice until I started buying decent hay.
Veggies: Piggies should get about 1-cup of veggies each day; fed as 1/2 cup twice a day. This is something you'll buy daily.
Toys you can buy (also available on TheHayExperts) vary from tunnels to houses to cosy cups for your pigs to snuggle in. You can get these from many piggie online stores and the ones available from P@H are also fine.
-- my suggestions on where you get your things from are based on my own personal dislike of pet shops. I avoid buying anything from pet shops and prefer instead of buy in bulk - which is also often cheaper - from suppliers.