The fonts that were made alongside TeX and which you see most often are the Computer Modern superfamily. For non-TeX use, I wouldn’t download those, but instead their offspring the Latin Modern superfamily, which you can think of as ‘Computer Modern Pro'—an enhancement, although still a work in progress. You get serif, sans serif, monospace, and odds and ends, and you get a selection of ‘design sizes’ (similar to Adobe ‘Opticals’ font families).
The simplest way to get Latin Modern may be to download the zip file, unzip it, then install the OpenType fonts (ending in ‘.otf’) that are in a subdirectory. You can ignore all the rest. You can also download the fonts individually.
(Because of its ‘modern’ style hairlines, Computer Modern/Latin Modern is difficult to use well at low resolutions, which makes me wonder why Donald Knuth designed a ‘modern’ in the first place. Perhaps because it was most suitable for his research aims [‘parameterizing’ typeface design]. Perhaps simply because he liked it. I suppose if I cared more I’d read the books.)
Also worth downloading for non-TeX use are some some revivals of Polish typefaces that the Polish TeX users group has made:
- Antykwa Torunska: http://www.janusz.nowacki.strefa.pl/tor
- Antykwa Poltawskiego: http://www.janusz.nowacki.strefa.pl/pol
- Kurier and Iwona: http://www.janusz.nowacki.strefa.pl/kur
The site also has some fonts derived from the ghostscript (URW++) fonts. As these fonts (unlike those above) don’t have characters for Esperanto, I haven’t taken much interest in them.