both of mine hated moses basket. we put them in cot in our room. lots more space for them, arms dont reach sides of cot...so dont wake themselves up.
baby number 2 has slept in cot almost from begining (i kept her in bed with mw for first month, breastfeeding after section was my excuse!).
our first baby has slept in bed (same reason), then slept in pram, until we got around to buying a cot and then moved into cot no problem.