Re: daybed or convertible for living room?
You might consider an adaptation to a futon. Instead of the back and seat coming out to a flat position the arms lay down. Either arm could recline giving the space a perfectly designed fainting couch. Both arms down would provide a very stylish sofa.
The choice is up to you. If you're looking for modern choose a convertible. If you're looking for old world charm, a day bed is a good choice. Multiple guests would suggest a trundled bed.
Storage needs would suggest a captains bed or a sleigh bed with 2 head or foot boards and extra pillows, allowing for storage beneath the bed.
One more idea:
I have a love seat with a matching storage ottoman. Turning the ottoman perpendicular to the love seat there is plenty of length to sleep and width to sleep. The key to this in my opinion, the ottoman does not slide easily, the feet are upholstered and will not slide on my carpet at all.
Debby in Oklahoma