'Paper Lanterns' is a named variety (cultivar or clone) of Japanese Larch, Larix kaempferi, the only way this clone is propagated commercially is by grafting. It is a nice variety, noted for being tall, narrow and being a heavy cone producer. It grows 7 to 10 inches a year, which is considered about "normal" for Larch. This is not a dwarf, it can be sized up to any size you need in a normal human's lifespan.
Grafted trees can be very good for bonsai, but they require special handling. Looking at the Conifer Kingdom website, if you did not read the details in the "about Plants and Pots Sizes" they do not say that their trees are grafted, except in the fine print under that heading. The #1, 6 to 9 inches, is probably 3 years post grafting, if the information in the "What do these sizes mean?" is correct.
The first trick to using grafted plants is to remember that the in the first year, these typical cleft graft will be barely stitched together. Bumping, vibration, freeze-thaw cycling in winter and any attempt to wire across the graft union can very easily separate the graft union, resulting in death of the scion. Second year is usually considerably more stable than the first year.
Usually by the end of the third growing season (year) the graft union has healed deep enough that it can be exposed to a normal winter. Still the graft is a weak point in the trunk, any wire across the graft union, depending on the bends you are attempting to create will put pressure on the graft and risk breaking the graft union. Until a graft union is over 5 years old do not even put wire across the union, even if only to anchor the wire, as the risk of putting pressure across the graft is always there.
About year 10, in most grafted trees, the graft union will be fully healed, and in most trees the union will begin to "disappear", and become hard to detect. It normally takes 20 or more years for graft unions to be totally invisible, but they become less and less obvious as the tree ages. The union itself will always be a weak point, but after year 10, one does not need to be as cautious, as long as one does not deliberately put pressure across the graft. Never try to "add movement" by bending at the point of the graft union.
The good news, with the scion 'Paper Lanterns' being of a more rapid, near normal growth rate for larch, the healing of the graft union should progress more rapidly once the tree puts on some bulk. And it should happen more quickly. You might not be able to tell it was grafted in as little as 10 years.
Actions I would recommend.
1. cut the little bit of green off on that stub from the understock. Do not try to cut the stub flush, if you have to put any pressure at all in forcing your tool in there. Wedging a diagonal cutters into the space between the stub and the scion can be enough to break the graft. Let the stub remain another 2 or 3 years, then you can cut flush. Just don't let any buds on the understock grow and develop as they will be "normal" larch understock, which might be Larix decidua, European Larch, rather than Japanese Larch. Usually commercial grafters will use one understock for all members of the same genus, regardless of which species the scion wood is.
2. If it were mine, I would put it in the "grow out bed" or a large container for growing out. You need enough growth to at least double, or triple the diameter of the trunk. Only by increasing the diameter of the trunk will the graft union heal and get stable. Also, a larger diameter trunk lends itself to an older looking bonsai.
3. For the 2020 growing season, I would do no pruning. Just transplant to your grow out container, then let it grow. In late summer, you can do some light pruning, but take off less than 25% of the foliage, you need growth. You can wire anytime late summer through winter. But while wiring be cognizant of the delicate nature of the graft union.
4. Repeat the pattern for 2021 growing season, limited pruning mainly in late summer, gentle with the wiring, encourage escape branches, escape leaders, you want the trunk to bulk up. Pruning off branches works against bulking up the trunk.
5. By 2022 or 2023 the tree might be ready for the very first styling. Or it might not. By this time you should have the experience (through this and other trees you own) to see a plan for the tree. At this point, year 5 or 6 post grafting the graft union will be much more stable. Now is the time you can be somewhat aggressive cleaning up any stub left over on the graft union. At this point you should have a good idea whether the graft union will become invisible in the future.
All in all, you have a nice piece of raw stock. I would be happy having it to grow out in my garden. Nice choice of cultivar. It will grow enough that "bonsai" will be possible in a normal lifespan.