Most commercial cages are too small, so a bin cage sounds like a good idea. Another option that isn't too expensive is a detolf if you have space (an Ikea glass cabinet tipped on its side with the door left off.
This is a list of Ikea stores in Sweden
IKEA group stores Sweden - IKEA
This is the detolf
DETOLF Glass-door cabinet - black-brown - IKEA
And some examples of set ups in a detolf
Ikea also make a large Samla bin that isn't expensive, for making a bin cage. It's 78cm wide by 56cm deep by 42cm high. But those are maximum measurements at the top and it slopes in a lot at the bottom. You wouldn't want anything smaller than that really. If you did get one of those, then ideally deeper substrate would be good so there's more of the floor area higher up.
SAMLA Box - IKEA
A glass tank is also good if you can get them (they are ridiculously expensive in the Uk). In Germany the welfare minimum recommended cage size for any species of hamster is 100cm by 50cm. In the Uk most animal charities recommend a minimum of 80cm by 50cm approximately, but 70cm by 40cm is considered minimum for a dwarf hamster (which is about what you would get in the Samla bin).
If you can give a hamster a tank with 20 to 30cm deep substrate they probably would dig a network of tunnels! Most people can't manage that depth of substrate, and hamsters do enjoy tunnel toys as well, but an area of deep substrate is good if it's not possible to have it deep in the whole cage or tank. Like on some of the detolf pictures some people have a third or so sectioned off and full of substrate as a digging area.
The main thing though is all hamsters need lots of enrichment in their cages. And that includes plenty of substrate (at least 4 to 6 inches - more if possible), a hide/house that they can retreat to, to be in the dark, and that's big enough to build a good size nest and bury some hoards (so the house is best if open underneath and sat on top of the substrate. Dwarf hamsters like the winter white should also have a sand bath - just a dish like a casserole dish with Chinchilla bathing sand in. And plenty of toys such as tubes and tunnels and little hidey places (cardboard is your friend! Cardboard toilet roll tubes, cardboard boxes with holes cut in eg). Some kind of cover - eg a shelf they can sit on or under (you can make a platform with just a piece of wood with dowel legs stuck on, or some people make platforms from Ikea knuff magazine racks).
Some of the set ups above and on the knuff shelf link will give you ideas for enriching the cage. Things to climb over, natural textures and so on. But low things to climb over really! As the others say, hamsters are naturally ground dwellers and diggers, they enjoy climbing things (although often that is just to see if they can climb out!) but aren't very good at climbing and can fall and hurt themselves.
Some good floor toys are the large cork tunnels you can get in reptile shops - they make a low hump to climb over and have a natural texture, and are also a nice big dark tunnel inside. Plus they are lightweight so would sit well on top of deep substrate.
They need chews to help keep their teeth trim and from growing too long as well.
And a wheel
Minimum 6.5" diameter. 8" diameter is fine too. Some dwarf hamster owners prefer a flying saucer. A wheel (or saucer) is really important though and they do need one as they would run miles at night in the wild and are very active creatures.
I think it sounds like a good idea to get one to start with and it will probably make taming easier too