I'm not the average player, cause I have had maps with nearly 1000 stations, but perhaps from my experiences:
Make it so like the train-stop chooser in Fat Controller mod.
That is also the TL;DR from below.

Cause for 0.14 I would like to have it like so:
Region and Purpose
I always name stations like
Main Base - Copper
Main Base - Iron
...
Mermaid Bay - Circuits IN
Mermaid Bay - Advanced Circuits OUT
Mermaid Bay - Plastic IN
...
That is a pattern like
REGION/NAME - PURPOSE/DUTY
This idea is lent from OpenTTD; there they have station names like "Hampton - Main Station", "Hampton - Wood" (if the station is near a saw-mill), "Hampton - Whatever". And I really think this is also very, very useful for Factorio, too. (Indeed the stops should have not each individual names, but that's a completely different suggestion, see
viewtopic.php?f=6&t=1528&p=11103#p11103 )
It can be assumed, that as a player I should know the region OR the purpose (or parts of that) to find the right station.
What does this help?
Assumed we (players/devs) can arrange with this (a station name contains region and purpose), then it follows:
We have three views to the list of train stops: Like current (all stations), Region and Purpose.
(It could be tabs or buttons to switch between these views. Not so important here.)
The All-view (like current)
- The scroll-bar is useless, if more than - hm - 20 stations found. I suggest instead a page, which displays me in a table-format the stations (e.g. 5 in a row and 10 in column, so it displays 50 stations per page) and I can switch between the pages by an alphabet-chooser and/or a pager. See Fat Controller's station select. Like so. This is also small in the beginning and will get bigger with adding more stations.
- See also other search options of the station selector in Fat Controller.
The Region view
- I want to have a selectable list of regions (here "Main Base" and "Mermaid Bay"). If I choose one, it opens all stations in that region.
- So this view is basically split in two parts: left is the list of regions, right is the found stops of that region.
- Now I also want to search my station on map. Open some map-view, type in first letters OR select from the found region-names and it zooms to the area, that matches my station names. I see then just the purposes.
The Purpose view
- This view is simply the same as the region view: List of purposes left, found stations right. Regions and purpose are just strings.
- A map view makes sense: Find all stations handling copper-purposes.
And with time I think into this direction: If the idea of regions/purpose works really good, then the game can replace text with icons. Instead of "copper" it can display the copper item. Instead of "IN" it can display an icon that displays a station with an in-arrow. The same with regions, instead of "MainBase it can display a part of map that is centered to then center of all "MainBase" stops.