We find silent spinners silent! But others do sometimes have issues with them.
For a syrian (the "varieties" are all basically the same), Souffle is right, you want an 8" wheel as the minimum. We use 11" and 12" for ours, but thats only because she's really fussy with wheels.
Personally I dislike flying saucers as I find they take up too much room in the cage, plus when we bought them we had a lot of problems, but if you want a giant amount of space taken up in your cage then they work too.
I'd stick to either a silent spinner, wodent wheel, or the trixie rodent wheels (aka cheap wodent wheels for buying when wodent wheels are out of stock lol), but thats my personal preferences and we've never owned a wodent wheel. Would have one... But yeah, they were out of stock and we needed a bigger wheel urgently so got the rodent wheel instead.
Oh and yes - All wheels do stay in our bedroom and are more than capable of disturbing our sleep if they're noisy. We have seven 6.5" silent spinners and they're great for not disturbing sleep, plus a 12" silent spinner and 11" rodent wheel in Scamps cage, and she never wakes us on her wheels either
And Jandr - Why are you now discussing roborovskis when the thread is about syrian hamsters? Oh and I don't know if they can use the 12", I've never offered either of Scamp's wheels to the dwarves because I er... really haven't seen the point... The 6.5" ones work fantastically for roborovskis and russian hybrids, and I assume Campbells and Winter whites too. I can't speak for chinese though. I also don't see the point in getting dwarves bigger - not because I don't think they can move them, I'd actually be surprised if Skip couldn't use at least the rodent wheel, and he's our smallest fully grown dwarf... But because theres no point in the wheel taking up twice as much space as it needs to.