Beauty
All bonsai are unique. There will never be another bonsai like the one you saw that you liked. Buy it or leave it, keep it alive or kill it, once it is found there will never be another.
What do you want out of it?
One cannot approch bonsai thinking it is a thing, an inert object, or a pretty mantle display piece. Ultimately, bonsai brings one closer to nature because one can experience the seasons with their tree, rather then ignoring the seasons with air conditioning and heaters. (Ironically, air conditioners and heaters are bonsai deathtraps.)
Where are you going to keep it?
All plant species and subspecies require different climates. You need to learn the climate of your bonsai space, and choose your plant accordingly. For example, a south facing condo deck can only take pines and junipers and that sort of high-sun tolerant plant. If you live in a basement, and your plant area is on the north side of a house under the deck, then you need a full shade plant like kingsville boxwood or fuchsia. If you live in rainy Seattle then you need birch or swamp cypress; if you live in Pheonix in the desert then you get mugo pine or english boxwood. (If you want the plant indoors you may be missing the point of communing with nature.)
How much time do you have to attend it?
Different plants require different amounts of maintenance. If you like to fiddle with things, then you should have high attention species like juniper and boxwood which require constant pinching; or you need willow or maple which require attentive watering. If this is you then having a pine - with irrigation so it needs attending three times a year for only a few hours combined, would drive you nuts. And you may start to dislike the tree. If you do like to ignore plants then a kingsville boxwood, irrigated, and in an oversized bonsai pot requres virtually no attention in any given year. (P.S. only if you are a one who gives high attention should you attempt indoor bonsai.)
How much experience do you have with plants?
Do you know how to keep a plant alive? Do you know how to fertilize? Flowering fushia requires good, and different summer/winter fertilization; and it requires winter protection. The pretty vegrigated japanese maple can only take so much sun, and is suceptible to fungal disease. But, the standard boxwood and the common pine are virtually imposible to kill, or to damage. They tolerate too much or too little sun, too much or too little water.
What "level" of plant do you want?
Are you looking for a cute tree, or a $20 000 John Naka original? You can get either. It is really about the tree you like. I suggest beginners get cheap trees, Naka said the price of admission to the school of bonsai is dead trees. But cheap is no indicator of finished quality. Bonsai art (and gardening in general) is a skill to improve the personal and monetary value of plants. Note: higher prices are indicators of artistic value, age, notability of the artist, and labor to form the tree.
Finally
Choosing a bonsai quickly is an interactive process: you find what is available, and pick from that pool of trees what would best suit you. You can only pre-pick the bonsai specifications you wish to have if you are willing to wait years while searching for or making the perfect plant.
My role in your tree
Nebari - Surface Roots
Nebari is the name of our business! We find only plants with good nebari. Good nebari usually means the roots radiate from the trunk evenly. The roots grip the ground, like in this picture. It may also mean that the roots are very visually interesting, if they are not radial.
Secondary Branching
The secondary branching should be visually clear. They should convey branchness or even trunkness, not twiggyness. They should be clean: branches don't have leaves on them, twigs do. Twigs are at the end of the branch. Much of the time creating/designing a bonsai goes into manipulating the branching. The purpose is to make the crown look good with the tree's best feature. (This tree's feature is the backward lean of the trunk.) Sometimes it takes years to get the branching perfect. That is one of your roles in your tree's life.
Crown
The crown should be full and even. This is the most easy, and most time consuming part of a bonsai. The crown on this tree gets an B+. The crown is full, and it is gently curved at the top. But this tree is still young. The branch tips will become more even. It will grow the small tertiary branches, from the secondary branches. That usually takes 5 years. And when the tertiary branches become to numerous, I could remove some secondary branches. Then this tree will be an A+.