To see what mobile service you have at the house, you can use pretty much any smartphone to check: on Android the application G-NetTrack Lite will tell you about the mobile environment, and on iPhone the field test mode (dial *3001#12345#*) also gives basic information on the frequencies and signal levels (works for Intel-based iPhones, for QC-based iPhones it's hit and miss).
To check speed, Speedtest is popular for checking latency and uplink / downlink speeds, but it may not give results relevant to the real world since network operators tend to have a Speedtest server in the mobile network to give optimal results. A better choice might be nPerf, which uses a bunch of real-world applications to give an evaluation of the network. OpenSignal is another useful application with coverage maps. You can swap SIM cards to check all of the operators.
Once you decide which operator to use, you should get the very latest possible 4G/5G WiFi router, so you will have the possibility to aggregate bands (Argentina has licensed bands 2, 4, 5, 7, and 28 to the operators for mobile service), use higher-order modulation and MIMO to increase your download speed. Bands 4 and 7 had the most spectrum allocated, so higher speeds are possible there. Band 28 suffers from interference and MIMO doesn't work well at low frequencies, so you get lower download speeds there. For the WiFi end,unless you need extended range, prefer 5.8GHz, since there's more spectrum and typically less interference than at 2.4GHz.
There are quite a few 4G WiFi routers advertised on Mercadolibre, the good ones aren't cheap. Fritz, HTC and NetGear have Snapdragon based equipment, and Huawei have some advanced 4G/5G CPEs.
