My Bona Fides: I am a retired machinist with about 50 years total experience with about 30 years experience owning my own shop. I would say that cobalt HSS drills are the best choice for what you want to do. Buying high quality drills will pay off in the end. Precision Twist Drill is a good brand. But any brand that MSC sells will be good. Don't be fooled by TiN coated drills. Even though the TiN coating is very good at resisting wear and is also quite slick it needs to be of sufficient thickness to work well. The problem is that there are a lot of cheap drills and other cheap cutting tools that have a coating that is way too thin to have any positive effect. So don't be fooled just because the drill has TiN coating, the drill must also be a high quality to begin with.
If you don't need a long drill then don't use a long drill. The best short drills are going to be Screw Machine Length, AKA Stub Length. The best point is a Split Point. These are the most common point for stub or screw machine length. They center better and require less pressure to penetrate the work.
You must use cutting oil for good tool life and least effort. Don't use motor oil, it is a bad cutting oil and will shorten tool life considerably. Any decent hardware store sells thread cutting oil is small containers. It has sulfur in it which is good for the high pressures encountered when drilling hard metals. There are better cutting oils but the stuff sold in the hardware store is commonly available almost everywhere. If you buy drills from MSC you can also buy some cutting oil from them.
When drilling tough steels to get the best results the drill must be spun at low RPM and the pressure must be kept high. There must always be a chip formed while drilling. It is best to keep the chips from being blue. If the drill stops cutting then either increase the pressure or stop drilling. There are lots of charts online that have the proper RPM for material and drill diameter. Use these for a guideline but try to keep the RPM a little lower. Remember, for your situation, it is better keep the drill spinning slower. This is because with a hand drill it is easy to get the drill spinning too fast. Also, when the drill starts to break through the work back off on the pressure. This will help prevent chipping the drill point.
So, to sum things up, use cobalt split point stub length drills, low RPM, high pressure, and cutting oil. And back off the pressure as the drill breaks through.
Eric