OK, a few definitions:
Yield strength is the amount of force required to cause the steel to yield, which means permanently deform (i.e. permanently stretch).
Tensile strength (a.k.a. "ultimate strength") is the amount of force required to cause the steel to actually break. This will be equal to or greater than the yield strength.
Minimum just means that the steel will be at least that strong.
Hardness is a measure of how resistant the steel is to scratching and denting. For structural usage it's probably not important, but would be important if you were looking for a durable finish, e.g. a workbench top or a tool bearing point.
Stiffness (you didn't ask about this, but it's another way of looking at the strength of a material) is a measure of how much something deflects when you put a force on it. Steel alloys tend to be pretty similar in this regard.
As you can see, "strongest" doesn't really have a specific definition, it depends on what you're looking for.
Here's an analogy for the difference between yield and tensile strength:
Imagine you have a spring. You pull on it a little, and when you let go it returns to its original shape. This is "elastic deformation", and no damage has been done. Now you pull hard on the spring and it doesn't return to it's original shape anymore. The material has yielded and you have "plastic deformation". This may or may not be considered "failure", depending on the application. Now pull really hard and the spring breaks. That's the ultimate strength. Clearly the spring has failed now.
As for the ranges: "steel" is a non-specific name for several alloys and it can be made in several grades, hence the ranges you've found. The material is usually designated with an alloy number. "Cold rolled" and "hot rolled" are methods for shaping the steel, and don't really tell you anything about the strength.
I should also point out that all of these properties that I've mentioned are for the steel material itself. If you want to know the behavior of an actual piece of steel, you need to know both its material and it's shape.
Think back to your high school physics class and use the Right Hand Rule.
Lay the drill bit across your palm, with the point towards your thumb. If the fingers curl around the bit (or screw) in the direction of the threads, then it's a right handed bit. That means you turn clockwise to drill (from the perspective of looking down on the work).
![enter image description here](https://i.stack.imgur.com/RzJFL.jpg)
This rule is also extremely helpful when you are working upside down and backwards trying to tighten something. Point your right thumb in the direction you want the screw or nut to travel, and turn the object in the direction your fingers curl to tighten.
When in action, Clockwise/Forward looks like this.
![enter image description here](https://i.stack.imgur.com/IP2q6.jpg)
Best Answer
Most drill bits sold are "high speed" drill bits intended for a variety of materials including metal (but not concrete, tile, glass or extended use in plaster or plasterboard).
If the bits are fairly sharp, you should be able to use them in the steel, assuming it is not a hardened alloy. To improve your chances, a bit of oil or cutting fluid at the cutting point will help prevent overheating. Slower is usually better.
The rust probably makes the steel weaker and easier to drill.