Most importantly to the future appearance of your stainless steel gas grill is knowing that not all stainless steel is created equally. In fact there are a large number of varieties of stainless steel. There is also the thickness of the metal that will impact how long your grill maintains it's appearance. If you spent $5,000 on your grill you probably got 16 gauge, 304 cold rolled stainless steel that has been polished to a mirror like shine. If you spend $500 you probably have something else. 304 stainless steel will clean easily and look great. While it will discolor under the heat you can keep it looking pretty good without a lot of effort. As long as the grill is kept from the elements, and kept clean you're fine.
However there is something called 430 stainless steel. 430 stainless steel, while technically stainless steel, will stain and rust. Yes, stainless steel can rust. This low quality stainless steel costs a lot less than 304 stainless steel so it gets used on lower quality grills either in part or completely. 430 stainless steel will need a lot more attention and care if it is going to maintain its appearance. 430 stainless steel, unlike 304 is magnetic, meaning you can stick a magnet to it so take a magnet and touch it to every part of your grill to see if you have 430 stainless steel. If you do you are going to need to keep these parts very clean and very dry. While this metal is basically uncoated steel that is very prone to corrosion you can keep it looking relatively good for several years if you take good care of it.
On the topic of every stainless steel grill not being created equally, some grills are completely welded and others are held together with pop rivets, screws and/or nuts and bolts. These fasteners may or may not be resistant to corrosion. I've seen nice shiny stainless steel grills with rusting pop rivets where the rust was running down the cabinet and legs of the grill. If you've ever tried to clean rust off something you know how hard it is, particularly if you've been told not to use abrasive cleaning materials. If you find fasteners that are going to be prone to rust, clean them good, make sure they are completely dry and then apply oil. The oil will help repel moisture and keep them from rusting. While it might take years for these fasteners to rust through they can leave large rust marks that will make your grill look bad.