If you process only the standard Lat / Lng pair, as you describe, and all you do is a simple search, then you may not be very dependent on increasing speed using a geometry type.
However, if you want to become more entrepreneurial, as you say, then exchanging for the use of geometry types will open up for you a whole world of new possibilities, not just search.
For example (based on the project I'm working on) you could (if it is uk data) load the polygon definitions for all cities / villages / cities for a given area, then cross-reference the search in a specific city, or if you have a roadmap, You can find which customers lived near the main delivery routes, highways, main roads, all kinds of things.
You can also do very bizarre reporting, imagine a map of cities where each contour was mapped and then shaded to show the density of customers in the area, some simple SQL geometry will easily return you an account directly from the database to calculate such Information.
Then tracking, I donโt know what data you are processing or why you have customers, but if you are delivering something, feed the coordinates of the delivery van, tell us how close it is to this client.
Regarding the question, is STDistance fast? well, itโs hard to say really, I think the best question is: โIs it quick compared to .....โ, itโs hard to say โyesโ or โnoโ if you have no way to compare it with.
Spatial indexes are one of the main reasons for moving your data to a geographically aware database, which is optimized for the best results for this task, but like any database, if you create poor indexes, you will get poor performance.
In general, you should definitely see some kind of speed increase, because the math in sorting and indexing is more aware of the purpose of the data, and not just linear in the operation, like a regular index.
Keep in mind that the wiser the SQL server, the better results you get.
One of the last things to mention is data management, if you use a GIS-oriented database, then it opens up the possibility for you to use a GIS package, such as ArcMap or MapInfo, to manage, correct and visualize your data, which means correction very easy to do by pointing, clicking and dragging.
My advice would be to create a side table for your existing one that is formatted for spatial operations, and then record some stored procedures and perform some temporary tests, see which one is better. If you have a significant increase only in the basic operations that you perform, then this is an excuse alone, if it is approximately equal, then your decision really depends on what new functionality you really want to achieve.