this is normal for babies. do what you can, but do not sleep in a pack and play, bouncy seat or car seat, they arent safe for sleeping. the basinette will be fine, but at his young young age, you can and should keep him in the room with you (at least for now!)
hes SO tiny and SO young, he doesnt even realize that hes a separate being from you yet. :) listen to YOUR instincts, you are mom, you have them because he is your child, no one else feels the way you do about him. :) so just tune into the things your heart is telling you. even if what your heart wants is something that seems "socially unacceptable" do it anyway, because you wont ever regret following your heart, but you will regret doing things you are comfortable with.
if your basinette has wheels, you can roll it around and put him in it wherever you are. theres nothing wrong with him being in there; i think my son was in his until he was like 4 months old? they are safe as long as baby isnt rolling over yet. :)
www.askdrsears.com is GREAT for help and resources.
so is www.llli.org (if you are breastfeeding)
just trust yourself. you know what you need to do, and best part is that you dont have to explain your choices to anyone that way. you dont have to say "well, so and so told me that i have to do this" nope. you do something because its just what your baby needs. :):)