if you are going to start with a newborn, you probably want to look at sized nappies (small, med, large) rather than osfm (one size fits most)

you can often get newborn or small nappies second hand in great condition. people sometimes change their mind (and don't use them at all) or they only get used for 4-6 months, and so still in good condition.

for newborns, i like prefolds with a cover (similar to the old style nappies you fold, but they have a middle panel that is already 2-3 layers so don't need as much folding) or fitted nappies with a cover.

when baby gets to medium size, i prefer ones that don't need a cover. so, either all-in-ones (aio s), pockets (where you put an absorbent pad in a 'pocket' of the nappy), or snap ins (where the absorbent pad/booster gets attached by snaps)

I am a bit of tight ass and never spend more than $15 on a nappy. I have bought heaps second hand, or get them on sale. Sign up to the nappy companies' newsletters you like, cos they all have sales fairly often.

darlings downunder sell different brands and have some good info and pics of nappies if you want some visuals of what each type looks like.