Changing table logistics

I’m getting a Dekor pail with washable cloth liners and I was wondering if it’s more convenient to have an extra hanging bag or some such thing - when you put the diapers in the pail, do you just drop the whole thing in, or do you remove the insert and put the diaper shell in one pail/bag and the insert in another? What’s the easiest way?

And I know you’re supposed to put solids in the toilet but our nursery is inconveniently far from our one bathroom. Should we suck it up and carry each poopy diaper there every time?