Whats the differences and options when choosing a cellular module?
LTE and GSM should not matter unless you are moving lots of data.  M2M communications usually involves small data packets.

I would not use the cheap USB sticks.

Multitech has some very good ones. Then there are the Multitech knock offs that are pretty good as well.  

Do not think a GPRS modem is similar to a dial up modem. Just because they both use the AT command do not let that fool you into thinking they are similar.  

The GPRS modem has a steep learning curve. In the 90s I wrote many modem apps. About 5-10 years ago I wrote a Windows texting app using a GPRS modem.  It took 2 years to get all the bugs out caused by unexpected tower responses or lack there of.  Do not expect the tower to always respond.  The tower will usually respond, many times delayed, and sometimes no response.

Given the high interest in mobile communications is it not strange that there are not more GPRS apps available? Ones that actually work. The reason is because it is difficult.  

These are what I have left of the ones I bought from China.  The have the old WaveCom chip.