Just wanted to add - unfortunately most commercial cages sold in pet shops are quite small, as you rightly said. Zooplus is a popular site for many members for buying cages online with free shipping. They are reasonably priced and the Alaska, Barney, Alexander and Kerry Terrarium are all popular. There is quite a good range out there, but usually means buying online. I did a video of my top ten favourite hamster cages earlier this year, which includes some of the popular ones - it might give some ideas. The main thing is to look at the size/depth and how good the access is. They may look plain empty but you can have tubes and tunnels as in cage toys which makes a more natural type of habitat for a hamster. Syrians tend to need rat sized toys and tunnels to avoid problems with tubes.
https://www.youtube.com/watch?v=JSKzn0g3sVk
The big word for happy healthy hamstercare these days is "enrichment". That means a variety of things
Depth of substrate (minimum 3 to 4" but ideally 6" to 12" or more. Most cages won't fit more than 6")
Plenty of places to go/things to do within a single area so the hamster can exercise and arrange their habitat (they like to arrange piles of substrate, dig tunnels and have hoards in various places).
A big enough wheel. 11" is a popular size for a Syrian and 6.5" to 8" for a dwarf hamster.
A good sized house that's dark inside - big enough to build a big nest so they can keep warm in winter. A tube or tunnel over the door helps keep it dark inside. They need somewhere dark to retreat to.
A sand bath.
Plenty of Toys - tunnels and hidey places (eg cardboard boxes, a plant pot on its side or other little hideouts).
A stone or terracotta plant pot base to help keep nails trim.
A shelf to sit on or under
Chews to help keep their teeth short
So enrichment is - the variety in the cage to prevent boredom, to allow the hamster to roam and forage and have normal behaviours.
You don't necessarily need a massive cage to have good enrichment, but with more space in the cage it can be easier to add more enrichment.