I would remove a chest of drawers from your bedroom to fit a full sized cot in, if it was me. The benefit of having something big enough to actually lie right next to baby in there is invaluable. I'd go so far as to say a cot bed is better than a normal cot, because they are bigger.
Bigger and more space in the cot is better imo, right from newborn. So it become a an extension to your bed.
Then remove one side off the cot (most are flat pack and this is easy to do) and wedge it up to your bed. This is more easily done in a smaller room because you can wedge cot up to a walk, then wedge your bed up to cot so they don't move away from each other.
A rolled up towel is usually enough to bridge the gap between the bed and cot mattresses.
On from this and if you are looking for what I view as 'the perfect option', try to find a drop-side cot bed. Dripside cots are not avaliable often anymore. They are considered safe and have the UK kitemark, but USA have seemed dropsides unsafe so few manufacturers make them now.
The resin dropside cots are great for cosleeping is they give loads of extra options.
Newborn - dropside removed, mattress heights match, cosleeper cot
Baby starts rolling - drop side back on but perminantly in dropped position. Mattress heights match. This gives a small 15cm barrier, still easy to reach over and comfort baby but defines baby's space as seperate to yours.
Baby starts sitting up - drop side still but perminantly in dropped position. Cot mattress dropped to middle height. Means you can still easily reach over the low barrier into the cot to settle, but baby now can't fall out when sitting up.
- Baby crawling - drop side back on but perminantly in dropped position. Mattress dropped to lowest setting but still next to bed. The drop side means it's much easier to reach into the cot while lying in your bed with your eyes closed and still half asleep
Baby pulling to standing - now you have to raise the drop side for safety. In the raised position the us feel the drop side is unsafe because of the risk of it unexpectedly dropping. So there was no risk when it was dropped perminantly. You could change to a non-dropside cot (your eldest cot?) at this point if you wanted.
Then start the process of moving cot away from your bed and eventually into baby's own room.
I realise I've written an essay. Sorry for waffling 