Hi, I run the NCT nappy library mentioned above. I do have a newborn kit for hire for £5 but it depends when you are due as it does have a few reservations. Contact me for more info and/or a free nappy demo.
Cheapest way to do it otherwise for a newborn is to get 3-4 tiny wraps and pad them with muslins or prefolds - you can get used prefolds for as little as 50p each if you search the dedicated facebook groups. Brand new wraps can be got from about £5 - try Twinkleontheweb and maybe TJs for bargains. https://www.twinkleontheweb.co.uk/acata ... ppies.html
https://www.twinkleontheweb.co.uk/acata ... RBO-1.html
If you can spend a little more, I like the Close Pop-in multipack, which is about £45 for 6 wraps and 10 inserts - you can also use muslins and prefolds with these wraps if (when!) you run out of inserts. Get the bamboo version if possible. https://www.babipur.co.uk/cloth-nappies ... -pack.html
If you want the most absorbant and least likely to leak then you need a shaped nappy with a wrap. Preferably bamboo, although these are slow-drying. Little Lamb are good and relatively cheap for this nappy type - the size 1 would last you up to about 9 months old. https://littlelambnappies.com/products/ ... -pack-of-5