Hi there and
to the forums!
I'm glad you've been doing your research, so I know any budgie would get great care from you. Although you know most of the information detailed above already, it doesn't hurt to review it in case you missed something
There's no such thing as too much knowledge!
I still am unable to see the picture. To post pictures on the forums, it's easier to set up a free Photobucket account and post a picture using the instructions on this thread:
It's up to you to decide whether or not you can provide a good environment for your situation.
I have a single budgie and I also am in school, she stays at home for a long time without me, but my family is there. She's been perfectly happy with this arrangement, however, since she is in a common area of the house where the rest of the family often watches TV or talks during the day, and keeps her company.
Is this room in your basement a place of high traffic? If not many people go down there (i.e if it is your room, or you're the only one who would be there) then I would not house any bird there unless there were more than one. Although birds are very social creatures, as long as they get plenty of human interaction, they can do wonderfully by themselves, as my little girl has, provided their personality is one that is more outgoing.
Let us know what you decide!