An unlocked phone will work in the US BUT if it is an iPhone, forget about ever updating your IOS again or using iTunes to transfer music or back-up. To unlock an iPhone, they jail break it here. I don't know if it can be done without jail breaking.
That depends on the carrier.
Nowadays you can unlock most iphones without jailbreak, by factory unlocking it or buying a r-sim to cheat the iphone into believing it's using its default carrier sim. That way you can keep updating it normally. My wife has a Sprint iPhone 5 with R-sim on iOS 7.0.4
Android phones are easier in my experience, you just have to check your bands to make sure it works on 3g with Orange or Claro. That's if you want internet from the carrier on it.
Orange Dominicana
Bandas de Frecuencia CDMA, GSM y 3G
CDMA N/A
GSM/EDGE 900 MHz / 1800 MHz / 1900 MHz
3G 900 MHz
Claro Dominicana
Bandas de Frecuencia CDMA, GSM y 3G
CDMA 1900 Mhz
GSM/EDGE 850 MHz / 1900 MHz
3G 850 MHz
As an example you check the AT&T GS4.
According to this page.
Samsung I9505 Galaxy S4 - Full phone specifications
It supports 3G on
HSDPA 850 / 1900 / 2100
That means that you can use 3G here on Claro but not in Orange.
By experience most T-mobile phones are compatible with Orange and At&t phones are compatible with Claro.
Although nowadays most verizon phones are world phones, means they have all bands unlocked, that's the safest bet to use both carriers here.
Went a bit overboard, just wanted to share and hope you guys learn something from this.
I usually buy my phones online and unlock them myself here. Smartphones are very expensive here.