For us at The Nappy Stash liners are an essential - however you don't need to use nappy liners if you don't want to. We LOVE the convenience of using liners, it makes clean up of poo so much easier and helps to avoid staining of the nappies. We use both types of liners are different times and occasionally use both fleece and paper liners at the same time (like when we are expecting a poo)! At night we use fleece liners when using a 2 part nappy to keep the wee man dry (this is important as most 2 part nappies don't have a stay dry layer).
Paper liners are usually either flushable or biodegradable. If you have old or narrow drains it is not recommended to flush liners, so in this case the best way to dispose of them is in a nappy sack in your bin. Reusable liners are washable, so solids should be dropped down the toilet or rinsed off and then put in your nappy bucket or wet bag with your nappies.