Moga Hero. The controller they released to replace this one:
http://www.amazon.com/POWER-MOGA-Hero-Electronic-Games-Game/dp/B00FB5R9OY/
I'm thinking pretty seriously about getting the Moga Hero $35 on Amazon right now. Gives you analog sticks and a Dpad. Also can charge your phone.
EDIT: PriceZombie says it's currently $40. I still see it at $35.
http://www.amazon.com/gp/product/B00FB5R9OY/ref=oh_aui_detailpage_o00_s00?ie=UTF8&psc=1 It's about the size of a 5 inch smartphone and is fairly thin. It's designed to be pocketable.
Is the Moga Hero Power much different? Looks like it's $24.99 on Amazon: http://www.amazon.com/POWER-MOGA-Hero-Electronic-Games-Game/dp/B00FB5R9OY/
I'm using this controller I got from Amazon.
POWER A MOGA Hero Power https://www.amazon.com/dp/B00FB5R9OY/ref=cm_sw_r_other_awd_hkCvwbN316G2Z
Works great, although it's very small. I'd recommend the bigger option this company offers for someone with big hands like me.
I don't what your budget is. if you already have a Xbox or PS controller laying around then i guess that the cheapest option would be a OTG cable like the one above. If you're going to purchase a controller then I think that the controller I linked is the cheaper. if you're going to try and stay around 25 bucks and want a dedicated android controller then maybe check out Moga Hero, it's on sale right now.