Having a limited budget, which 2-3 out of the 24 Avenir Next typefaces are most useful for web design?
This is a very personal choice, but in terms of having variability... I'd choose the ultralight for a title in big boxes (it would look great with a solid background a big font size). Demi or Bold italic are stronger and have more "character" (in my opinion!) so I'd use either of them for page titles (main title, perhaps. It looks good above
And I guess you could have a regular for smaller titles like
h4 and for general use in the page. By the way, I'm sure you know this, but you can't distribute these fonts in the website using @facefont, so they would only be in images. If you use GLP (free open) fonts instead, you can have them in the website and redistribute them (depending on the license, but it's generally like that).