As has been said, go for layers. You can certainly tuck them in tightly in a moses basket. Sophie has a growbag but I've not used it yet as she was far too small for it even though it says from birth. I tend to opt for cotton sheets and cellular blankets too
If you're getting a moses basket, have a think about buying a separate, better mattress. The mattress that came with ours was very thin and went all saggy in the middle quite quickly. We opted for the 'top of the range' moses basket one from Mothercare which cost about £25 but is layered like a proper cot mattress with the breathable bit zipped on. It's much firmer and feels more comfortable to the touch.
Sophie is 4 months today (wow, just realised that!

) and she's probably got another month or so in her moses basket before she outgrows it.
Good luck hun
