EDIT: This is 3/4G related, not picking up WiFi that may be nearby!
I did quite a lot (and still do) with mobile data for work. We have various combined ADSL/vDSL and SIM data modems so if your broadband goes down it falls back to SIM data as you are doing with your MFi devices. We also have a need to provide workers with a way to connect to the internet when out of the office, this is the bit that is what you are all doing.
Firstly, if where you are does not have a phone signal then it doesn't matter what you have with a SIM card it won't work. You would need some expensive satellite setup and the data satellite we have used can be down if its too cloudy, rain, snows or is there is a S in the day it seemed!
Next most important is that you can receive whoever signal is available where you are. You will all have been in places where you have a poor signal but someone else has full bars, the way to get that is have a SIM card that will roam. That means it will switch from poor signal on say an EE mast to a strong signal on a 3 mast or anyone else who is better. If you type roaming data SIM in to Google you will find lots of companies who offer these so if you need it look for the best deal for your usage in countries you are travelling in. The companies we have used deal in blocks of 100 SIM's minimum so no point posting here. If you have any connection to a communications company you may find they will provide you with a suitable SIM or two though.
It then comes to how and what you need to connect. If you only use a single smartphone or tablet/SIM enabled computer then put the SIM in and away you go.
If you want to connect to more than one device you would normally either use some sort of wireless device that takes a SIM card (
MiFi type) or turn your phone into wireless hotspot (also called tethering).
At work we no longer use
MiFi or 3/4G dongles to connect to the internet we just tether our phones. Everyone who needs to do this has a company iPhone although our Android fans say you can do exactly the same with them. When there was a mixup a year ago Christmas with my home broadband switching I put my phone in the window (extremely low to no signal area) and could just get 1 bar, this allowed both me and Caz to connect our macs and use the internet. As a guide our home broadband is under 3mbps (yes when you stop laughing we are in the sticks) and the phone on 1 bar was much quicker than our broadband.
So: Check if you can tether, if so you dont need a
MiFi or anything else, UNLESS you have a large area to cover and won't be in line of sight of the phone you tether to, then get a
MiFi or similar.
If you have used aerials on a
MiFi and have any data that can actually prove it has made a significant difference I would be interested in seeing it as I have some installations that may benefit. In our experience aerials have made little to no improvement except in situations where the SIM card/wireless signal is shielded or in a metal box (I kid you not).
Lastly, I am no expert in this. I do systems and server support for a small company and as such we are expected to have an answer to everything and to provide it for nothing. If money is no object there is kit that will make a difference but for most folks we haven't found it yet but as I said if someone HAS then I would like a pm