The most important rule with Syrian hamsters is... one hamster = one cage.
Syrians are strictly solitary and must be kept on their own once they reach maturity. If left with another hamster in the same cage, they will fight to the death. Don't worry, they won't get lonely on their own.
Once you get your hamster home
For the first day or so, try to leave them to settle into their new home and get used to the new surroundings and unfamiliar smells. After this you can start to handle them, and make sure to do a basic health check for any illness or injury. Use the food that is supplied with your hamster, and if you can, try to keep with the same brand ('Harry Hamster')
The first few months
Try to get the biggest cage you can afford. They will be fine in a smaller cage at first, but I recommend upgrading once they get a bit older.
Recommended: floor space of at least 70cm x 40cm (cages: 'Alaska', 'Hamster Heaven' or 'Barney', available from Zooplus.co.uk)
Not recommended: Modular type cages such as Rotastak. They are difficult to clean out, lack ventilation and there is no space for a large enough wheel.
I would recommend waiting till your hamster is at least a few months old before giving them a wheel full time. You can start to introduce one but as they are still growing, it's best to wait, as they can get addicted to them! Make sure the wheel is big enough for them to comfortably run in, and not arch their back (about 7 or 8 inches is usually sufficient). I am a fan of the large enclosed plastic wheels, and any wooden wheels, as they tend to be quieter. (Both are available from Zooplus)
Continue to feed extras as well as their normal dry mix. I have been feeding them extras such as vegetables (broccoli, carrot, sweetcorn, cucumber) and baby food (mine love the 'Heinz' ones, particularly the ‘creamed porridge’ and ‘sunday lunch’). Just give them a small amount every day, and reduce the frequency as they get older.
There are a few choices of bedding available. The cheapest is just to use torn up toilet paper, but you can buy shredded paper or what looks like little pieces of 'J-cloth'. Never use cotton wool bedding - it is extremely dangerous. Even though some pet shops sell it and it says it is safe, it is not. It can be ingested and get blocked in their intestines or wrap around limbs and cut off blood supply.