When I had my first daughter some......years ago, we used sheets and blankets tucked into the Moses basket/cot/bed* (*select appropriate bed size for age) and that was the end of it.
When I had my, now toddler, some 3 years ago, we discovered that this particular little lady did not conform to being tucked in. In fact, the only time we actually tucked her in was in her Moses basket! This was purely due to the fact that she could not move around as she was simply too small to do so, but she still used to kick the covers off her feet in the night so she needed constant checking. OK, that sounded like harder work than it was but even leaning over the side of the bed to peer in at her laying next to me was tiring at times ;-)
When she got to around 5 months old, sheets and blankets were hopeless. She would kick them off and end up laying across the cot or upside down. I was more worried about her disappearing under them and getting too hot than her getting a bit cooler. I had even tried putting the sheets across the cot instead of the way they should go just to give more tuck-in at the sides but nope, she still got out. No matter how much I tried to tuck her in, she escaped - usually within minutes!
This is the point I looked at other things that would keep her warm and found Grobags :) Brilliant. Why did I have about 20 sheets and blankets in my airing cupboard when I could have one or two of these? I immediately went out and bought two Grobags, one 2.5 tog and one 1.0 tog. These are now known as the "Day and Night" set. My daughter seemed to love her Grobag and settled down to sleep in whatever position she liked - upside down or sideways - and I knew she would be warm. There was no danger of her getting it over her head as it's got poppers on the shoulders (adjustable) and zips up to under her arms. Perfect!
The other thing you need to consider, of course, is access to little bottoms in the night when they are so tiny and the Grobags have this sorted with zips that undo from the bottom to the top across one side so that you can open it up completely to get to your little one without disturbing them too much. If they wake in the night you don't even have to get them out of it for a nice cuddle :)
Of course, I have bought some cheaper 'Grobag style' bags and they have been OK but you really don't get the quality unless you buy the real thing. Yes they cost more but you do get what you pay for. They wash and tumble well so you could even make do with one (although two really is best just in case of accidents).
We used our Grobags up until my toddler was almost 2 years old when we moved her into a toddler bed and bought a duvet set. Our baby now has the Grobags and we're about to buy her a new one for winter. A definite must for parents of wiggly little ones :)