If you are starting with an .epub file, there is an editor program in the Calibre suite which can change anything in the .epub, including the fonts:
But if you convert the file from .epub to .mobi, with any program including Calibre, it's then almost impossible to edit the resulting .mobi file. So you get stuck with whatever default font the conversion program has specified in the conversion process.
The .mobi reader program on your computer (e.g. Mobipocket Reader v6.02) will let you apply any font that is currently installed on your computer to the .mobi file, regardless of what font the .epub file specifies (in effect, the specified font is simply treated as the default setting, hence you can impose a different font in your reader program).
But if you transfer the .mobi file from your computer to a kindle, the kindle will probably only have one choice of font, a default that can't be altered. With no user option to choose a different font, you can only change the font size on the kindle, but not the font itself.
I only have an older kindle, admittedly, but the design philosophy is clearly to deprive the user of the ability to select a font. The kindle comes with what is an attractive and easy to read font, and the manufacturer doesn't want the kindle to get a bad reputation by allowing users to set up fonts which look less attractive, or which might be harder to read within the limitations of the kindle's hardware.
The kindle is a cheap device to buy, because of its extreme simplicity. And part of the business motivation of the manufacturer in not including fancy fonts with it is to avoid the cost of paying licensing fees for the use of such fonts, all of which have a commercial cost - a fee will be due to someone who owns the rights in the fonts. Fonts that look nice always belong to someone.
It might be possible for the user to tamper with the kindle's default font, by delving into the program code using specialist hacking tools. There are plenty of such tools. I've used some of them, even though they use a commandline interface of no mean complexity.
But I don't have any idea how to do that particular bit of reprogramming.
If what you want is a device that gives you a choice of font, you might be better off buying a different device, even a small tablet, that allows a choice of font.
Any device on which Mobipocket Reader v6.02 will run would meet your needs, because as I say that program has easily configurable settings that can apply any font you have on your computer to your current choice of .mobi file (without needing to change anything in the .mobi file).