Definitely check out the Nappy Lady's website as mumtosp suggests. She's very helpful.
www.thenappylady.co.uk/
I've been using cloth for 2 months now and wish I'd started sooner. My DD has very sensitive skin and reacted to most disposable nappy brands. They don't smell as much either.
I think some studies assumed a 60 degree wash every time, then tumble dry and even ironing them!
I'm in a flat too and use pocket nappies with mostly microfibre inserts for daytime. I find the 'shells' dry overnight and the inserts in 12-24 hrs. I have a few more inserts than nappies.
For nighttime I use a 2 part system with bamboo nappies. These take at least 48hrs in my flat so I need 5 with washing every other day. They would dry quicker if I could hang them in my airing cupboard or in front of a sunny window. These last me through the night with an older baby, you'd need more for a newborn. You could use microfibre nappy with bamboo boosters for extra absorption.
Preloved is much cheaper. I've heard the Cloth nappy tree mentioned and Facebook local selling pages.
Fill Your Pants do a £10 nappy trial
www.fill-your-pants.com/
I did this, it was great to see what brands suiting my dd for fit, ease of use etc.
Other sites I like are:
Little lamb - like their Facebook page as they often post discounts there
www.littlelambnappies.com/
Fluff heaven - often have good deals
www.fluffheaven.com/#home
The clean green nappy machine have a 1/2 price tots bots bamboozle stretch mini pack at the moment
www.cleangreennappy.co.uk/kits/day-packs/tb-zs2dp7
And if you did want to splash the cash check out dimplebum
www.dimplebum.co.uk/
Or don't... It's hard to resist 
HTH - also read the nappy chat threads, the posters on there are lovely and very helpful.
Oh and congratulations!