What is camera lens stabilization?
Stabilization avoids camera shake (when your camera is unstable), and therefore is not useful if you use a photo tripod for example.

This is especially useful if you're using a long focal length, which is more prone to camera shake.

This technology also allows you to reduce your shutter speed a little by two notches (or more) without having any blurring issues, which can be useful in low-light situations.

Stabilization is not insignificant, I recently advised a friend against buying it because of that: an attractive offer with an 18-55mm whose version without stabilization has a bad reputation, and a 75-300 with which it could only have taken sharp pictures in ideal light conditions (which never happen when you need them, obviously).

Note: more and more often the stabilization is integrated into the case (especially with hybrids). If this is the case with your device, the presence of stabilization on a lens is secondary in your choice. That said, some brands combine the stabilization of their lenses with that of the body to make it even more efficient, so let's say it's not useless either.

What is a tropicalized lens?

A tropicalized lens or case is protected from bad weather (dust, humidity, splashing water). This results in the presence of seals at the junctions (buttons, hatches, lens ring), and also often in a more robust construction (eg metal, especially for housings). Attention, this does NOT mean that your device is waterproof and that you can play in your bath with it.

Where it gets a little complicated is that the tropicalization does not correspond to any single standard, so each manufacturer does its own cooking a bit. For example, the tropicalization of a Sony A7III is a notch below that of a massive Nikon D850.

Several useful points for you in practice  :

  • Tropicalization can be useful if you shoot a lot in aggressive environments: sea, sand, snow, etc.
  • Tropicalized equipment was much less common in the time of film and has become more popular since the advent of digital. Therefore, don't be paranoid either, great photographers have traveled the world before us without a tropicalized case, so it's going to be fine.
  • You can do without it most of the time if you're careful. In any case, it should not be the determining criterion in your choice in my opinion (unless you are a professional or you go for months in the bush like Mike Horn)

In this regard there is a textbook case. You go from a very cold environment to a warm and humid environment (typically when you return home in winter): remember to put your equipment in your bag before returning, and leave it inside so that it warms up gradually. If you subject your equipment to this thermal shock, fog will form on the lens, but above all there is a risk of internal condensation in the lens and the device (water and electronics do not not a good household).

Which camera lens brand to choose?

There are bad lenses from the brand of your camera, and good ones from third-party brands such as DZOFilm and Tamron. And vice versa. My principle is simple: I am looking for a lens of the brand of my camera. If ever I can't find what I'm looking for, I look for third-party brands.

For some models, it may be preferable to turn to third-party brands as the differences in quality are minimal and those in price significant. It's up to you to see if there is a substantial saving to be made by reading the tests on the internet.