I've never used an unlocked phone, so I can't really vouch for them. But if you want AT&T LTE service on Straight Talk, they offer the ZTE Unico at Wal-Mart. With this phone, during the late early morning hours (slightly before 5:00 AM EST), two speed tests came back faster than 60Mbps. The fastest of the two was 67Mbps, but during the day when everyone's phone is on, the speeds understandably drop.
At work during the day, I can't get a good signal from AT&T, because the nearest cell tower is one mile away and there's nothing but forest between the two sites, so the signals are minimal. No service or signal issues with Verizon LTE or CDMA with Straight Talk, except the speeds are limited (CDMA limitations) or throttled (LTE).