Here are 30 of the Best Fonts / Typefaces that every designer must / should own sorted by alphabetical order. There are 15 serif fonts and 15 sans-serif fonts. These fonts will last you your whole career!
A brief description of what each font is best suited for is provided however are not limited to this.
There are some top free cool fonts that are downloadable in this collection and some that come with your operating system… the others are not so free but they sure will help you improve your typography! They include original PC, Mac and Truetype fonts.

15 Serif Fonts

What does serif mean?

1. Adobe Caslon

Magazines, journals, text books, corporate communication.

2. Adobe Garamond

Textbooks and magazines

3. Bembo

Posters, packaging, textbooks.

4. Bodoni

Headlines, text, logos. (I couldn’t get big preview for this font.)

5. Clarendon

Dictionaries and headlines.

6. Courier

Tabular materials, technical documentation, word processing.

7. Excelsior

Newsletters, Reports, Proposals.

8. Lucida

Low resolution printing, small point sizes, reversed out half tones.

9. Minion

Limited edition books, newsletters, packaging.

10. Perpetua

For displays with fine lettering, long pages of text, chiseled text.

11. Sabon

Books and corporate communication.

12. Stempel Schneidler

For displays and fine publications that need a legible text type.

13. Times New Roman

Newspapers, magazines, corporate communication.

14. Trajan

Books, magazines, posters, billboards, anything to do with the ages or religion.

15. Walbaum

Magazines, journals, text books, corporate communication.

15 Sans-Serif Fonts

What does sans-serif mean?

1. Akzidenz Grotesk

Large Signage, all purpose for print media.

2. Avenir

For books with large amounts of text

3. Bell Centennial

For listings and very poor printing conditions.

4. Bell Gothic

For very small amounts of text that contains large amounts of information.

5. DIN

For signage, posters and displays.

6. Franklin Gothic

Newspapers and where available space is limited.

7. Frutiger

Large signage, all purpose font for print media.

8. Futura

Large displays, small text in books.

9. Gill Sans

Signage, all purpose font for print media.

10. Helvetica

Large or small text, all purpose type figure.

11. Meta

Text, number, especially corporate communication.

12. Myriad

Large displays, all purpose media.

13. Trade Gothic

Newspapers and classified ads, advertising, multimedia.

14. Univers

Packaging, signage, text books.

15. Vag Rounded

Instruction manuals and print advertising.

Source: From the book “30 Essential Typefaces for a Lifetime” by Imin Pao and Joshya Berger. A history of typography is also found in this book as well as more information on each font and the designer.