You don't need anything apart from a bit of washing up liquid in a bucket of warm water
. The small pet disinfectant by beaphar and johnsons is fine, if rinsed well afterwards and left to air so it doesn't leave too strong an aroma. But that is only needed if there's been ilnness or disease. For normal cleaning you just use warm water (I sometimes don't even use soap in it). If you use soap water, again rinse well to remove any residue or scent.
But for a general clean I just wipe the inside of the cage base with a soaked cloth.
Vinegar isn't a full disinfectant. It will kill some bugs but not all. So it's not a substitute for disinfectant. It's a cleaner. So not much point really and it still leaves a strong smell which can take some time to wear off.
The only time I used vinegar to clean a cage (which probably wasn't necessary) was after our hamster had been left at another house while we were on holiday, with his cage, and he went a bit bonkers when he came home and couldn't settle - very stressed. After about 10 days I decided to do a full cage clean in case he could still smell the other home (which also had hamsters) and it was upsetting him. That did the trick. I used the vinegar to remove the scent on the cage. Afterwards he turned his nose up at the smell (even though well rinsed) but settled straight away.