Some fonts are optimised for print (the vast majority), other are optimised for screen display (e.g. Verdana, Georgia). Some work reasonably well for both. Not many though (Calibri springs to mind).
There's no amount of tweaking you can do to make a font look good on screen if it's only intended for print use.
I'm a bit of a purist when it comes to web design. Unless your site is an artistic statement in itself, where pixel-perfect placement is essential, I always think it's best to keep it as simple as possible. If you specify fonts, make it tried and trusted, universally available fonts.
I have a hunch that what you really like about the AListApart site is the design, including the line leading for body text and the use of white space around the text. I don't think it's the fonts. Look at their CSS file:
#content .ishinfo, #content .title, #content .byline {text-align: center;}
#content .item, #content #ishintro, #ishoutro {border-top: 1px dashed #999;
padding: 1.5em 1em 0.5em; margin-top: 0.75em;}
#content #ishintro, #content #ishoutro {padding: 1em 1em 1px; font: italic 1.05em Georgia, serif;}
#content .title {font-size: 1.8em; text-align: center;}
#content .byline {padding: 0 0 1em; margin: 0 0 1.25em; text-align: center;
background: url(/pix/byline-separator.gif) 50% 100% no-repeat;}
#content .byline a {font: bold 0.85em Verdana, sans-serif;
text-transform: uppercase; letter-spacing: 2px;
margin-left: 0.25em;}
#banners {margin: 0 20px 20px;}
#banners li {margin: 0 0 10px;}
#banners li a {background: #CCC; display: block; width: 173px; margin: 0 auto;}
#banners li img {background: #CCC; display: block; margin: 0 auto;}
#banners li a:hover, #banners li a:hover img {background: #666; border: none;}
#choice {border-top: 1px solid #D9D9D9;
padding: 1.5em 20px;}
#choice h3 {color: #333; font: 0.9em Verdana, sans-serif;
text-transform: uppercase; letter-spacing: 0.33em;}
#choice .title {text-align: left; font: 1.5em Georgia, Times, serif;}
#choice .byline {display: block; border: none; text-align: left; margin-top: 0.5em;}
#choice .byline a {font-size: 0.8em;}
#choice .info {font-style: italic; font-size: 0.9em;
color: #666;}
#sidebar {width: 140px; padding-left: 15px;}
Nothing unusual there. Verdana, Georgia, Times....