I have a box at home--not a priority mail box--just a plain brown box that when it was mailed to me was sealed with priority mail tape and a priority mail stamp(well it's sort of like printable postage I guess) (it was from a yarn company). I've been able to remove the priority mail tape and can most likely cover the priority mail label (or maybe even remove it). Is this okay for me to use this box?

If it's just a plain brown box, yes you can reuse it for any class of mail you want to.  Just make sure to remove all the Priority tape and any labels or markings that say Priority Mail.  If it's a Priority Mail address label on it, be sure and remove the part with the Priority Mail logo on it.

Thanks! I was able to get everything off of it. Surprisingly the tape came off pretty easily as did the label. I was hoping I'd be able to use the box.

I don't understand why the title of this thread is about Priority tape when all of it was able to be removed?

You can use ANY type of packaging as long as it is not UPSP Priority or Express packaging. That includes: no removing or taping over the areas that say Priority or their Priority logos. No turning the Priority boxes inside out to reuse. The USPS recognises their own boxes.

You CAN use any other packaging even if it was originally sent to you as Priority mail, or from UPS, FedEx, DSL, etc. if you remove all evidence of the other shipping labels, barcodes, etc.