Baby needs a place to play as much as to sleep. A crib or a traveling playpen can be both.
I used a bassinet on coasters for the first three month of my babies' life. They slept or played in it during the day and evening, when I didn't carry them in a sling. At night they slept next to me. Bassinets come in at least two mattress sizes. Mattresses are thin foam in a waterproof vinyl or poly covers. When the baby gets heavier, bassinet is not safe any more: it can topple. It is not meant for a baby who can raise its head and shoulders.
I had a crib for a place to keep older baby safe, asleep or awake. Standard crib is actually big enough for a three year old, and if you don't like keeping a toddler in a cage (through I can't imagine why you don't), a crib-size mattress fits a toddler bed. We were still co-sleeping until 8-12 month of age, and a crib was more like a playpen. There are co-sleeping attachments on market. Some are like Snuggle Nest -- a low box with three soft walls, which you put in the bed; others are like a crib with three sides, leveled with your bed.
My friends used Graco portable crib as a playpen. It folds in a three feet-long bundle and fits in its own bag if you use it as intended. If you stay with friends in a non-baby-proof house, the baby is safe there. Most hotels in the US have portable cribs, but many babies don't sleep well in beds they are not used too. It turned out very useful piece of furniture: while it is not occupied with a baby, it's a natural place to pile the toys. Their daughter is five now, but they still use the playpen in that last capacity.
See also: children, newborn baby, jogging stroller, baby high chair, baby travel checklist.