If you need something quick drying then you cannot beat microfibre shaped two part nappies or pocket nappies.
Microfibre is a manmade fibre which is an issue for some people (not me ). It will come out of your washing machine almost dry which is fab. It is very absorbant too.
A shaped two part nappy will need a wrap over the top to keep it waterproof - motherease rikki or airflow wraps are the most reliable for most people. With shaped nappies (i.e those that look like a disposable made from cloth) chubbiess is not too much of a problem but the tallness will mean you need a nappy with a decent rise.
Downsides are some brands of shaped MF nappies are a bit bulky under clothes.
Pocket nappies are a waterproof bit with a fleece bit inside - between the two parts is a pocket into which you can stuff whatever you like. You stuff the pocket and put the on the baby. Take the insert out when you wash and wash both the insert and the nappy in the same way. The nappy bit dries very quickly without tumbling and if you use microfibre inserts they will too. These are easy to put on as only one piece but they can be prone to leaking if the fit doesn't suit your DDs shape. Pocket nappies are usually thin fitting and you can boost the pocket as needs dictate so for a long journey just pop in two boosters etc
Microfibre can hold smells if you don't do a cold rinse in your machine before you wash them. Doesn't happen all the time but some people have problems with this when their LOs are teething etc and the urine is more strong than usual.
For grandparent and DH proof nappies go for velcro (aka aplix) fit. Two part nappies and pocket nappies are just as easy to put on IMO despite one being only one piece to attach to baby!
Have you looked to see if you have a local nappy project that you can hire to try out and see what suits best. Also your council may offer you financial incentives to change to cloth.
Lots of good advice to be found on here