Hello Asako,
Librarian and amateur audio engineer here.
Depending on what your budget is, you are going to want to focus on: 1) a decent microphone, 2) an audio interface (to connect the microphone to the computer), and 3) isolation (not only from noise that bleeds in from outside of your recording environment, but also from room reverb which can muddy your audio). The microphone is by the most straight-foward of the three to understand/achieve, as isolation may not only include selecting an ideal space but treating the room with absorbers and diffusers as well. Some microphones plug directly into your computer via USB and you can skip purchasing the audio interface. Some of these may actually be pretty good too, but in my experience, I have never come across a USB microphone that produced as clean and loud of a signal as the traditional microphone/interface combo did.
I would spend exactly zero dollars on audio recording software, because there are already a lot of really great tools (like Cakewalk for PCs/Macs and Garageband for Mac users) that are completely free. These digital audio workstations possess editing (trimming audio, fades in/out, etc.) as well as really high quality audio effects (compression, EQ, reverb, etc.) to process your audio. If you can't afford (or understand how to implement) room treatment, you may wish to spend a little money on an audio plugin which you can use in the digital audio workstation to remove room reverb.
As important as buying the right gear is learning how to use the gear correctly. Here are some good YouTube videos on techniques to make your podcast sound as professional as possible.
If you have any more specific questions, feel free to email me directly. I know that some companies sell podcasting kits (usually a microphone, an interface and headphones) and I would be happy to opine on those or any other gear you are thinking about.
Best of luck.
Steven