The best bin for a bin cage is the really useful box 145 litre - about 80 x 60 cm - has good depth and easy to cut. The minimum floor measurements are ok but you wouldn’t want to go any smaller for a Syrian. My preference for Syrians is a large front door - good for interaction and taming - rather than tank style with top access. So I prefer cages like the Savic hamster plaza - 100 x 50 cm. that is ideal for a Syrian and has a big front opening door.
There is a Pawhut cage you can adjust to have a front opening door (the angular shaped one) by reversing the door and front panel when you build it, do the door is at the top instead of the bottom and allows for more/deep substrate too. However the danger with wood cages is some Syrians will just chew their way out.
If you like the idea of diy though, have a look at the Linmon cage tutorial on YouTube. That is melamine so can’t be chewed out if - but the cost will be higher than just buying a Savic plaza! I prefer to spend more on good cage contents like a large labyrinth house and a silent runner wheel
. (Which can be attached to bars wherever you want it).
Not sure if the Savic plaza is in stock again though.