I know a bit about materials in a general sense, but am far from an expert. I do know that a simple high carbon steel makes for a good quality blade, but the needs of sword blade are different from the needs of a scalpel or a pocket knife or a large Bowie or an axe head. So the specifics of what carbon content is appropriate depends on what kind of blade we are talking about. I suspect that one is not always given the option of telling a maker what kind of steel they want their blade made from, and likely have to accept what the maker feels is appropriate. That being said, a little research can help inform whether or not the maker has made a good choice. If you can find out what steel has been used, you can google it and often find summaries online of the steel qualities, as well as opinions of folks in the industry and martial practice as to whether it makes a good sword blade.
I point out that simple carbon steels make excellent blades because there are a lot of exotic steel alloys that also make exceptional blades, but can become quite expensive. I feel that some people get a bit hung up on finding that “perfect” steel for a sword, and I am not convinced that the “perfect” steel exists. There are a lot of good and appropriate choices, and you don’t need the most expensive exotic steel in your sword, especially if it triples the price of an item that would already be excellent. I will say that a lot of modern blades are made from 5160 spring steel, which is the same steel used to make leaf springs for truck suspensions. That is a good quality, flexible and tough steel and is recognized as a good choice.
As far as heat treatments, some steels respond better to different types of quenching baths, water or brine or oil. I’ve not heard of an acid quench. I have heard of acid etching and an acid bath meant to highlight the grain of the steel for aesthetic purposes. At any rate, the type of quench depends on the type of steel, and that is something the maker needs to be knowledgeable and skilled with. That is the kind of thing that I think you need be be willing to trust the maker because you have no control over it, so choose your maker wisely.
For katana type swords, I have heard that Paul Chen/Hanwei Forge makes affordable, quality items at the entry level. Take a look at them. I have no personal experience with them, but it is a place to start. If you are going to be taking seminars from a good teacher, see what he recommends.