Taps are made of W, O, and A tools steels, and HSSs. And a lot more for specialized uses.
You haven't specified the problems sufficiently.
Is this a one-off that you are making for yourself? Or a product you intend to sell?
--> One-off suggests not worrying about material costs as much as machiniabiity and heat-treat stability, and toughness (get A2)
Will this be used in a hand-tapping operation or using a tapping machine or a drill press with a tapping head?
--> Machine operation - consider HSS
How many times will this tap be used (and what duty severity will it see) in its lifetime? Chasing two holes in cast iron in a vintage machine tool , or threading as many new holes as possible in 304 or Ti? Will you be tapping hardened steels?
--> Here, others are more expert that I. But horses for courses.
One thing to be aware of is that a tap is not just a hardened bolt with grooves. For any type of duty cycle at all, the threads must be relieved.
Assuming you get the tap forms relieved properly, can you get away with "as machined" and hand finished taps? If not, how do you propose to grind the thread forms? Here's a thread on tap grinding:
Tap grinding
Unless you really are Jonesin' to spend a half a year learning to cut, heat-treat, temper, and grind taps (and want to make or buy the equipment needed to relieve and grind the tap) it may be worth having the tap made. Don't want to crush anyone's dream, but I'm just saying don't expect to goof around in the shop for couple weeks and come up with a commercial-grade tap.