These suggestions are generalizations.........it is always best to let your personal taste be the guiding influence.
Your perspective of a lamp changes according to height of furniture lamp is sitting on. When replacing a lamp shade, place lamp on piece of furniture it will permanently be placed on or on something the same height. This provides the best perspective of how replacement shade fits the lamp.
Lamp shade proportions should reflect lamp base proportions. For example: a short squat lamp will look best with a shade of similar proportions.
Using the same lamp shade base shape, round or square, provides a cohesive appearance.
For Safety: there should be a minimum of 3-1/2” between lamp shade and incandescent bulb unless using compact fluorescent bulbs.
When looking for a new lampshade an exact match size may not be available. It is often possible to correctly use a shade that is slightly taller or shorter. To solve this issue change the harp, which holds the lamp shade. Harps are most often 2 part which enables the height portion of the harp to be easily switched. Choose a larger size harp if the shade needs to be raised up or a smaller harp if the shade needs to be lowered.
It is normally best to choose a slightly larger than smaller size shade when trying to select a shade that does not match your requirements exactly.
The lamp shade should sit at the appropriate height on the lamp. Lamp mechanics should not show. Ideally shade base should be just below lamp socket. Lamp shade should cover lamp socket but not base of lamp.
Lamp harps support most harp type shades. Most harps are detachable, made up of a bottom wing piece and top harp-shaped height piece. This enables the main harp section to be removed from the base. Changing the height of the harp most often solves the problem of the shade not sitting at the correct height on the lamp. If the shade is sitting to low on the lamp base – use a taller harp, likewise if the shade is to short on the lamp base use a shorter harp.
Harp shades are also used on 1/8 IP shade holders and some lamp socket clusters. Some of these holders offer shade height adjustment. See picture left.