Different fonts have been created for different purposes, and you should select a font depending on that purpose.
Helvetica and Times, for example, are common fonts that have been created to be easily readable in print. Arial and Verdana, on the other hand, were created specifically to be easily readable on a screen. Both Arial and Verdana look ugly in print, while both Helvetica and Times are more difficult to read on screen.
Another difference is wether a font was designed for body text or for headlines. Headline (or display) fonts are often more ornamental and difficult to read than body text.
There are other kind of font (e.g. fonts to imitate hand lettering in comic books, or OCR fonts meant to be read by machines) and you must first identify your usage, before you start looking for a fitting font.
Besides the purpose, a font has a character, that is, it looks playful, light, earnest, etc., so different fonts with the same purpose – e.g. different fonts to print body text – will fit a different kind of text. Usually academic journals prefer a more sober looking font, while novels sometimes use a font with more character that will support the story.
All (professionally made) fonts can be used in professional publications. Which font is the appropriate one for your publication is a question that typographers, typesetters, book and web designers have been trained to answer.
As a professional writer, the most professional descision would be to let a professional book or web designer pick the font that best represents your writing to the intended audience in the chosen medium.