Most of the conifers, that is the evergreen, needle-bearing trees, such as the pines, spruces, firs, junipers and cypresses, and also larch which is not evergreen but is needle-bearing, respond very well and look centuries old in a matter of a few years, if treated correctly.
Some of the broad leaved trees which drop their leaves in winter can also be grown, for instance, beech, Japanese acers, crab-apple, oak, birch, ginkgo, willow, rowan and elm, as well as shrubs such as japonica, cotoneaster, pyracantha, and even the climbing wisteria.
These trees are all hardy and in fact they must have cool conditions outdoors in winter when they are dormant. But you can also grow some of the more tender plants as bonsai, for instance, Ficus diversifolia, F.benjamina, Pittosporum tobira and the citrus species (lemon, orange, etc), and there is no reason why you should not experiment with other slightly tender house plants of a tree or shrub nature, using those which are reasonably slow-growing.
One sometimes sees a bonsai grotesquely stunted and shaped; this is not really the aim. You should try to obtain a perfectly proportioned small tree, with its top growth and main trunk in balance – you should have the impression that you are looking at a normally sized, fully grown tree through the wrong end of a telescope.
Sometimes the poor shape is because the bonsai has been grafted by the nurseryman in an attempt to hurry up nature in order to sell the specimen quickly – growing true bonsai is not the way to a swift fortune. You can usually pick these out, however; the graft is out of proportion to the rest of the tree, and at an awkward angle, and the bonsai often has the top obviously cut off when the tree was some years old, rather than pinched out at the seedling stage.