Hy,
there are lots of t-sensors on the market. If you need more the temperature (like humidity, CO2 etc.) maybe www.elsys.se is worth a look (no, I get no provision…).
Gateway selection depends much on the location and the network. We have used one low cost gateways (like the ttn-GW 868) with good very coverage in an old building with about 5.000m², but a second gateway as a backup may be a good idea (and is not very expensive). There might be other reasons to choose a different gateway. For example, we have not been able to log in to eduroam, as they have a slightly different login procedure that was not supportet.
You can use TTN to set up an integration, but we found it much easier to use node-red as a relay. You can have node-red running behind a firewall and connect via MQTT (or the TTN-Node) to get the data. This makes it very easy to filter and manipulate your data before connection to your app.
Currently we have node-red running on a cloud server, which is not expensive and very convenient to handle. We found also that influx-db performs very well on the same server and is easy to integrate with node-red and TTN.