Absolutely, both TransPennine and Northern trains stop at Oxford Road.It's possible to go straight to Oxford Road station instead of Piccadilly? That's way closer. Also what's the best way to get the train tickets? via an App or...
I thin the best is to buy a ticket at the airport train station; theoretically, it's a little cheaper to buy them in advance online, but... it would be like 4 GBP vs. 6 one way... It's up to you : )