First, I'm going to mention that the Droid DNA battery is replaceable,
just not easily... though, it's not for the faint of heart and technically handicapped. Manufacturers want you to pay big bucks to replace batteries or buy new phones instead of replacing your own battery. It's just another form of planned obsolescence.
Second, I would definitely recommend staying away from the Moto E/G/X line for many of these reasons now, especially due to battery life and the difficulty to self-replace for most folks. I had hoped for better from their batteries, but time has only reinforced my pessimism. Used should be perfectly fine if the phone's been well cared for or refurbished, and it's a model with a user replaceable battery.
If you want a "good" camera (which is pretty subjective from a smartphone standpoint), you need to stick with high-end "flagship" phone models, or the big expensive name brands that get advertised on TV - Samsung Galaxy, HTC One, etc... except most of those don't have user replaceable batteries.
Now, regarding the carriers mentioned... I'm guessing you're thinking of switching to Ting GSM (T-Mobile) and not Ting CDMA (Sprint), correct? The following bit of advice will be tailored to that point.
Key AT&T network service bands:850MHz CLR (band 5) & 1900MHz PCS (band 2) 2G GSM bands
(end of life January 2017, already offline in many parts of the country)850MHz CLR (band 5) & 1900MHz PCS (band 2) 3G UMTS/HSPA+/WCDMA bands850MHz CLR (band 5), 1900MHz PCS (band 2) & 1700/2100MHz AWS (band 4) 4G LTE bands
(secondary LTE bands for non-700MHz LTE markets)Key T-Mobile network service bands:1900MHz PCS (band 2) 2G GSM band (limited coverage in most markets)
1900MHz PCS (band 2) & 1700/2100MHz AWS (band 4)
3G UMTS/HSPA+/WCDMA bands (3G AWS bands are being taken offline in all markets to be refarmed to 4G LTE use in 2015/2016)1900MHz PCS (band 2) & 1700/2100MHz AWS (band 4) 4G LTE bands
(LTE bands are actively being built out and replacing all connectivity on the 3G AWS bands)Why share with you all this information? So you know what to check for to get the right band support for both AT&T and T-Mobile MVNOs. It gets really messy and complicated getting into high speed data and the 700MHz LTE spectrum between providers, so we'll focus on the most important baseline to work with to ensure reliable phone reception and decent data speeds with both networks:
850MHz and 1900MHz UMTS/HSPA+/WCDMA (3G GSM). (This last part in bold right here is really the only
major thing you need to remember from all those bands, numbers and abbreviations.)
Most all carrier unlocked AT&T branded phones will work well, as will most carrier unlocked T-Mobile branded phones manufactured 2013 and newer, but it never hurts to know the specific bands to aim for as well.
Now, here are the two phone finder tools that I know of that tells you if the battery is user removable, or lets you search by that criteria:
http://www.phonescoop.com/phones/finder.phphttp://www.phonearena.com/phones/fullMake sure to use the advanced search tool with both, but don't feel obligated to check everything off. Just look for the features that matter most, and either select the AT&T and T-Mobile carrier options or specify the key service bands mentioned above. Phone Scoop lets you search by user replaceable battery, but does not have a granular band search tool. Phone Arena has a granular band search tool, but only lets you search for "non-user replaceable" batteries, so you have to leave that option deselected and check the overview to see if you can replace the battery or not.
Speaking of, since Gadfly mentioned the Nexus 5, its battery is
not easily user replaceable.
As for future support, make sure the phone can at least run Android 4.x for the sake of security updates.
Why teach you how to find a phone on your own instead of just recommending one or two? You know exactly what you want, we don't. Also, self sufficiency is useful. Heap on the fact that user-replaceable batteries are becoming more rare, it's best to just show you how to find weird exotic combinations of features in a smartphones on your own.