You could chown, but I've run into problems with that on external sites.
I've started using chmod, just to make the file have 777 permissions after it's uploaded, this way I can do whatever I want to it without any trouble. This is not the most secure way to go about it for sure, if someone else on that server has access to your directories and files, they could in theory modify/remove your files as well. Just keep that in mind.
This is the quick of it. Upload it, and after you move it to it's final resting place:
chmod($saveDirectory . $fileName, 0777);