What is the recommended way to copy my data from a windows disk to a linux disk?

I have one hard drive which just has my data (no applications). I am
currently on windows 7, so the file system is ntfs.

I want to migrate to Linux on my second computer. The disk is USB
drive, so I can just move it and plugin it the second computer running
Linux. I understand that Linux can read NTFS disks.

But I want all my data to be on the linux file system, not NTFS. I
have a second blank disk I want to use to copy all my data from my
NTFS disk, to the blank linux disk and move everything to be under /

What is the safest way to do this? The data is about 1 GB. The new
blank disk is 3 GB, so space is not an issue.

I need ofcourse to mount my NTFS disk from linux as read only (to be
safe), and then do the copy to linux disk so that everything lands
under /usr/home/me/ on linux.

What would be the best way to do this? just cp -R or do I need to do
something better? Do I need to do this as root? but I want all the
data to belong to me the user and I do not want to mess up file
protections and all that on linux since things are different there. I
want to do this right first time and not have to go fix things later
as the data is very large.

thank you