Small vs Tall - the problem with trees, like puppies, is that they grow up. While they may start life all cute and cuddly it's not long before you could have a monster on your hands wreaking everything that you once enjoyed about your garden.
A small tree is one that will grow to about 5-8 feet. Medium sized trees usually don't exceed 15-20 feet and tall trees can break into the stratosphere like the sequoia - well almost.
So, when you buy a tree, choose one that will fit within your surroundings in 10-15 years not just on the day you plant it.
Evergreen vs Deciduous - do you enjoy raking leaves? No? Then stick with an evergreen. For the novice, a deciduous tree is one that loses its leaves during winter while an evergreen...well...remains evergreen.
Exotic vs Native - There has certainly been a trend over the last decade to search out indigenous tree species rather than their exotic counterparts. The reason, I guess, is that natives take far less effort to maintain and if they're already growing in the region then there's probably more chance of success.
Exotics - I'm using this term to describe trees that you won't find growing in your area - can often take longer to establish, are much more prone to local diseases and pests and are usually more expensive than natives. But then the rewards of growing exotics are that you can show off your own individual talents and produce a garden that is distinctly different from your neighbours.
Fruit vs Ornamental - an even greater trend is starting to develop in the tree buying arena than just the popularization of natives. It seems that more gardeners are planting fruit trees over ornamentals as their garden plots get smaller and as the desire to be more self-sufficient grows.
Ornamental trees are wonderful, in that they provide beautiful aesthetics to the garden but enjoying the produce from your own fruit tree is hard to contend with.