I loved diddy diapers when DD was small as they were cheap, fit well and even the cotton ones didnt take too long to dry. I dont have a tumbledryer either so my nappies are always dried outside or on the clotheshorse indoors - i keep one especially for the nappies (its just like 3 flat rectangles that fold out) so theres always space for them.
pocket nappies are great as the outers dry very quickly, and the inserts can be put on the radiators to dry. In an emergency shaped nappies will usually dry overnight on a radiator but dont do this too often as it can damage the elastic over time. Pockets arent always great at containing explosive newborn poo, but fuzzi bunz have been known to be great for small babies! but you will probably need boosters for them as their inserts arent very absorbent. Flexitots are meant to be an absorbent, quicker drying option than bamboozles, but ive never really liked the fit of them
The best thing to do really is make sure you have enough nappies (or you could wash everyday, but its not the first thing a new mum wants to do!) bulk up with cheap terries or prefolds, or preloved nappies!
hope LO arrives soon so you can have fun with the nappies!