Pay version of the app

Make the current app a pay version and release a limited version for free. A lot of people would be happy to purchase this Awesome app!

don't. I wouldn't even be able to purchase because of google play's need for a credit card... better add a donate button in the settings or something like that

Well, there should still be a payment method to pay these guys!

I think rather than adding a paid version, Keep it free, but use PayPal donations. I'm sure there are a lot of people who use this that would be happy to donate. Do not limit AirDroid or you'll lose alot of customers who may not be able to purchase or even afford apps from Google Play (I know I wouldn't be able to afford it, The only reason I have an Android device was that it's a gift and it's not on a phone plan.)
Donations would be the best way to go. They can still receive money that way as Bjoern said.

I'd actually prefer to have both a free full version on Play, as well as a donate-version there too, but paypal might also be cheaper?

I would like a pay version just to hide the recommends tab!

I would have to be among those whom are against AirDroid having a paid app, especially on the Play Store. Not lots of people have credit cards (including me). But I have a PayPal account.