I'm an ios developer and created an app which allows the user to add different texts and reposition them.
I would like to provide my users with a premium feature which is a font pack. I'm looking for a few free fonts that I could embed in my app and require payment for them.
What kind of license am I looking for?
As most "Free" licenses, I.E Creative Commons, Apache, MIT and GPL, only allow further free distribution under the same license and most also require attribution or disallow commercial use. I think you may struggle to find a commercial use font that doesn't have restrictions or added requirements and may find it easier to buy a cheap fontset for a one-time fee that comes without restrictions.
The only exceptions I am aware of is the CC0 License and the SIL Open Font License. Although the SIL Open Font License clearly states that fonts must be packaged with software if they are sold. Obviously not being a lawyer I couldn't say if a font pack would count under the license as independent software and also how you would allow the user post-installation access to the font outside of your application.
To ensure that you don't unknowingly breach copyright you should check, and keep a copy of, the license provided with the font alongside the time and place you obtained it. You should also adhere to the conditions set forth in the agreement.
http://search.creativecommons.org/ is a great place to find such content but unfortunately they do not feature fonts. http://www.fontsquirrel.com/ on the other-hand is a great place to find free fonts although you may have to trawl through a few to find one with a license that fits your use.