Hi there. They need a good amount of floor space and not too much height, when looking at cages. The Alaska, Barney and Alexander cages on Zooplus are all good options. The Alaska and Barney come with Syrian sized houses and good shelves as well - all you need then is wheel and toys.
Hamster Cages | great selection at zooplus
Carefresh is fine but can work out expensive in larger cages. Fitch is popular on here - you buy it in bulk and it works out much cheaper (it's recycled food grade paper and very similar to Carefresh but less dusty). Or hemp bedding from Zooplus is popular too. Our hamsters have always liked Fitch.
https://www.fitchrecycling.co.uk/ani...-delivery.html
One of those bales lasts me about 6 months with a 100cm Barney cage and spot cleaning mainly. You can afford to be more generous with it too as it works out cheaper. The bag isn't too big to store indoors (and it needs to be kept indoors so it doesn't get damp and mouldy).
You want a good depth of substrate to cushion any falls from a height. At least 3 to 4", ideally 5 to 6" or more. An 11" wheel ideally. A good hamster mix with enough protein and all the nutrients (you can't go wrong with Tiny Friends Harry Hamster).
Nesting material - best is plain white toilet paper torn into strips.Don't use any fluffy bedding.
I'd recommend getting a litter tray and Chinchilla bathing sand as well. They will use a litter tray if you put it in the place they choose to pee - often a corner of the cage. I use this one. It's a good size for a Syrian
https://www.amazon.co.uk/Hamster-cor...=hamster+potty
The sand soaks up the pee and you empty the litter tray every 5 days or so and it helps the cage stay clean.
Don't do big clean outs weekly. You can spot clean mostly and use the litter tray and that way you only need to do a full substrate change every 2 to 3 months. The more substrate there is, in larger cages, the less often it needs clean outs. Even then i replace some of the old clean substrate and mix it in so it smells familiar. Also clean wheel a different week and any other items a different week again. That way something always smells familiar and it avoids stressing them. And don't use scented things to clean out - warm water or soapy washing up liquid water is fine unless there has been illness or disease. So no need to use disinfectants or other scented products. If you do need to use a pet safe disinfectant then rinse well and let the cage air so the scent goes away as it bothers them.
Think that's about it! Oh and most toys sold for hamsters are too small for Syrians and some are quite dangerous as well. So avoid toys with chains or open ladders. Rat sized toys and tunnels are better for Syrians, or just home made ones like a tissue box.