What features to look for in a replacement gear cabling?
For better or for worse, Shimano has been pushing coated cables as the default option for their road groups for a while now. There are two 10-speed Tiagras; 4600 came with normal uncoated stainless cables and the more current 4700 comes with Optislick cables, their more basic coated option. All the 11-speed groups come with some type of coated cable.

Coated cables aren't strictly necessary but are more a response to the fact that with smaller cable pull numbers comes increased sensitivity to friction. The same is true for lubricated housings, which are a mixed bag in that compared to running cables dry, they will tend to make things work really well up front with the downside that over time the lubricant can attract and hold in contamination.

One of the compounding factors, which also prevents a universal answer, is that a lot of bikes have bad cable routing and need all the help they can get to have functional shifting. Coated cables absolutely help in these cases. STIs with under-the-tape shift routing always have some extra friction to contend with, and depending on the bar and mounting position it can get pretty ugly, another reason for coated as de facto.

If you're working on your own bikes then there's little harm in trying basic stainless slick and seeing how you like it. If you need to maximize performance up front then coated is basically how you do that.

Putting a new cable in an old housing in a pinch is fine if you need to replace it because of fraying or a kink or something like that, but housing is cheap, has a major impact on performance, and the philosophy of pre-lubed modern housings is pretty much to replace it liberally to keep performance up.