You dont need a basket, but lots of people have them so they can have the baby with them all the time, we used one for the first 14 weeks, up until my baby was 12 weeks she stayed downstairs with us and took her up with us, after that i started putting her up on her own, now she is in her cot and goes up on her own at bedtime.
I know lots of people who put lo straight into a cot, its personal choice :-)
I borrowed a moses basket and my son was only in it a couple of weeks because he was so big lol
Its up to you, there is no problem putting them straight into a cot.
Just remember "feet to foot" -always put your baby at the bottom of the cot with their feet at the end so they cant wriggle down under the covers
the way i did it was was to use a moses basket inside the cot untill he grew into the cot, i always felt my son woulsd get lost in a big cot when he was tiny so thats how i compromised.
My first was in hers for ages and it got loads of use, my second went straight into her cot. If I had a third I don't think I'd bother with one actually.