This article is from the Bicycles FAQ, by Mike Iglesias with numerous contributions by others.
A word or two about racks and attachments. Stability and strength are
your prime considerations. I have had loads shift and break loose in a
number of ways. I have seen racks bend, break, and sway. A rack should
have a firm mount to the bicycle at as many points as is possible. It
should be of firm and rigid construction. Look for triangulation in the
legs - the struts should be mutually supporting. Quality 3-point mounted
racks are almost as good as quality 4-point mounts. Brazed-on 4-point
mounts are the ultimate.
Single point mounted racks and flimsy racks are only suitable for very
light loads. The only exception to this is using one of these racks to
keep a Carradice bag off the rear wheel.
Trailer attachments are either on the seat-post or the rear triangle.
Mine is on the seat-post, and I've never had any reason to be unhappy
with it. Mostly you want strength in this attachment.