Info is pulled from
PCMag.com
GSM = CDMA = LTE in the sense that they are all radio systems (technologies)
Carriers use either GSM or CDMA for 4G (as displayed on some AT&T phones that are not LTE) and below.
AT&T and T-Mobile use GSM
Sprint, Verizon and U.S. Cellular use CDMA
GSM can use voice + data at the same time (means you can talk on the phone and google an answer)
CDMA cannot.
Partially pulled from
Wikipedia
LTE is a different beast, it's based around GSM/EDGE and UMTS/HSPA technologies and provides a higher speed than your typical GSM and CDMA networks. It also works alongside those networks. So back in 2007-2012 when choosing the right carrier was that important, as the emergence of the iPhone and Android phones brought simultaneous data and voice to the limelight, most people tended to jump towards AT&T for the GSM network because, as stated above, it could do that.
LTE is still in its infancy but people have been working hard to get voice over LTE (VoLTE), once it matures and VoLTE is available, it won't matter which carrier you go to. They are working on it because they end up saving a lot of money by being able to phase out the older GSM and CDMA towers in favor of shiny new LTE towers. (Less running cost)
If you get a GSM phone you can only connect to towers for voice calls that transmit GSM signals (AT&T and T-Mobile towers, roaming on the off network that's not yours at really low speeds)
If you get a CDMA phone you're stuck with CDMA towers, roaming on the other carriers.
LTE towers provide access for both, but you'll still roam on LTE networks if they don't belong to your carrier and the speeds will be just as slow as roaming on GSM or CDMA).
TLDR; if you want voice and data at the same time, limit yourself to AT&T(good network) and T-Mobile (ehh network), if you don't care Verizon is a great network but the bill is a bit over priced compared to other carriers, Sprint has some of the cheapest bills but they also don't have an extensive network like Verizon or AT&T.
I'm open to corrections on this, but this is what I remember from 3 colleagues who deal with cellular networks quite a bit.