I use a Google/LG Nexus 5. It is a relatively cheap phone that can still kept up with some of the higher-end ones from 2013-2014. Granted, the camera and audio may not be as good as an iPhone or Galaxy, but I haven't found anything to complain about. For the price, it is very hard to beat. Too bad that Google decided to go with an expensive phablet (albeit still cheap compared to the 6 Plus and Note 4) for the Nexus 6.
If you go with Verizon, I would very much advise looking into the Motorola Moto X. I have heard a lot of great things about that phone and sort of regret not being with a carrier that has it.
After that, it is sort of hard to mention any well-known phones. If you're concerned about the iPhone 6's price, then that would probably also rule out the Samsung Galaxy S5, HTC One M8, LG G3, and Sony Xperia Z3, since those are about as much as an iPhone 6. I'd advise staying away from any Windows phone for now, since they really don't have the same app support that Android has. BlackBerry's problem is arguably worse, and their CEO is...yeah... [http://www.forbes.com/sites/erikkain/2015/01/22/blackberry-ceo-to-congress-make-blackberry-apps-mandatory/]
I guess you could also look at some mid-range Android phones. I've heard some good things about Samsung's mid-range phones, even if they don't sell well.