Choosing a Signal Booster/Repeater for proprietary devices

I have been shopping for signal boosters/repeaters on the lower end (cheap to mid-priced.) There is a plethora of specs given on products in order to help choose the correct device that sometimes seem conflicting, overlapping, possibly redundant or just confusing. I often see specs given as:

(Note, I am in North America)

Frequencies (850 MHz etc)
Bands (2, 5, 12, 13, etc)
Carriers (Verizon, AT&T etc)
Generations (3G, 4G etc)
Acronyms which describe either channel access methods or technology protocols (GSM, CDMA, LTE etc)

Unfortunately I am not supporting a cell phone where I could just call up my provider and have them tell me the technology or acronym description to look for. The devices I am trying to support are proprietary secure tracking devices and it is difficult to get information such as acronym designations, frequencies, or bands for them. The only information I have on them is the carrier (either Verizon or AT&T) and they are 3G.

In order to try and simplify things, I am wondering if repeaters/boosters are strictly repeating radio waves, agnostic to:
acronym designations?
carrier?
generation?

In other words, if I know the frequency (or band) I need, carrier and generation, and I find a unit that supports that, do I need to concern myself with acronym designations?

Or taking it a step further, if I know the frequency (or band) I need, and I find a unit that supports those frequencies, do I even need to concern myself with carrier, generation, and acronym designations?

Or does the technology and encoding protocol also need to be supported by the booster/repeater as well?

I have tried contacting booster/repeater vendors, but have not had any luck in getting any information at all on this.

I have researched the various acronym designations as best I could, indicating channel access methods and/or technology. While they all seem to indicate a technology, it seems they also may or may not to be an indicator of either frequency or generation. I have attempted to distill the information for designations below, based on North America standards:

PCS - F: 1900 MHz; Generation: ?
GPRS - F: 850 MHz; Generation: 2G, 3G, ?
GSM - F: 850, 1900 MHz; Generation: 2G, ?
EDGE - F: ?; Generation: "pre-3G"
CDMA - (Channel access method) F ?; Generation: 3G, ?
LTE - Usually refers to "bands" which can cover a plethora of frequencies, seemingly applies only to 4G?
DCS - Seemingly a generalized parent protocol covering various frequencies and technologies

If someone could help me to sort this out, it would be much appreciated. As stated I don't have the luxury to be able to just call up my provider and have them tell me the technology or acronym description to look for. So I am trying to get a general understanding of what are actually the pertinent factors which apply to the devices themselves.