The first couple of weeks we were on about a two-hour feed, sleep, nappy change cycle, she'd sometimes sleep a bit longer at night but she was a bit jaundiced and we were told not to let her sleep more that four hours in a row, not that that happened more than once! So I'd say we got through 10-12 nappies a day. Nowadays at 20 months + it's more like 6-8.
She was 8 1/2 pounds and was still in newborn size babygrows for the first 2/3 weeks, so I'd guess it was one of the smaller nappy sizes too, but you can make a good guess on the weight ranges and be aware different brands use different weight ranges so you need to check. At 41 weeks I was pretty sure she wasn't going to be tiny so could be fairly confident which range she'd fit into but don't forget they'll always grow into the next size up and you can always go to the shops.
We used cotton wool and water as that's what the hospital wanted, they didn't even like water wipes, and I'd say we did that for maybe three weeks though I'd switch sooner or try cheeky wipes earlier on a second child.
One odd thing though: the hospital and nurses wanted us to keep an eye on how many wet nappies she has in 24 hours for the first week or ten days, I think because she was slightly jaundiced, and we found it was harder to tell than you'd imagine: pampers had an indicator line that turned blue when it was a wet nappy and we found that really helpful. I had assumed we'd use lidl or Aldi nappies but friends had done a baby pack for us including pampers and we realised a) the indicator strips on pampers were way better and easier to read and b) she had nappy rash using anything but pampers and water wipes. She still does at 21 months, I tried again recently to switch.
The cheaper ones are really good for most people but it's worth checking if there are rashes etc- using pampers, water wipes and bepanthen her bum was perfect except for maybe one dose of nappy rash during teething but as soon as we tried to switch brands she reacted. I'm hoping any future babies have less sensitive bums!