Congratulations
Tiny twins are hard work, but it is so so rewarding to cuddle two warm babies in your bed 
We pushed a normal cot with the side down up against the side of our bed. The two babies then slept across the cot (mostly, though they did fit side by side in the normal direction for a fair while :) ). They stayed that way until about 4 months, when I started to cosleep for the majority of the night.
Personally, I would have found it too difficult to 'keep track' of two times in the bed during the really early days as a) I was very tired, b) I wasn't used to cosleeping and c) the babies were very helpless. By 4 months, the were able to move away if they wanted to, and I just felt more with it and safe enough to cosleep.
Until the babies were about a year old, we had the king sized bed to ourselves (DH in the spare room). I wouldn't have coslept with all four of us in the bed while they were younger, as I think It would have been dangerous for the baby between DH and I and we wouldn't have had enough space. At about a year, we got rid of the cot, which made room for a single bed to be added to the side of our king size, so then there was enough room for four (and the babies were that much bigger again).
Bed guards are your friend! We still have guards on our bed now, and our twins are two! They would still roll off the bed if we didn't have the guards, as despite our king+single sized bed, a baby still has to sleep close to the edge.
Good luck, and don't be afraid to try stuff. You will judge what feels safe and can tailor ideas as you go 