I've been using the Meshtastic site planner (https://site.meshtastic.org/) to plan out my mesh before committing to anything. Among other variables, you can plug in the antenna gains/heights to get a good idea of what your coverage will be (though it is just an estimate). A 6 dBi antenna and a few meters of height can go a long way from the results I've been seeing. The biggest factor is line of sight, so getting your gateway node up as high above the "smaller" nodes will give the best results regardless of which antenna you go with.
if this is the correct wording
I think "gateway" is the more correct term. From what I've read in the docs, "router" is usually used for nodes configured with the "router" role (which is different from a node connected to the internet via MQTT). In most cases, it's recommended to just keep all the nodes in "client" role since the "router" role behavior can be counter-productive in many cases.