Historically it was the dormant season that was chosen for this, because transplanting during the growing season was apt to kill. Having tried pot-grown trees over the years, I have come to two conclusions. The first is that the short-term gain is outweighed by the fact that they do not do so well in the long run. The second is that I am loath to pay extra for a pot and compost that I don’t want! So, for me, tree planting is a late-winter activity involving bare-rooted plants.
Fruit trees usually come in two parts, with the fruiting part grafted on to a rootstock. There is a wide range of rootstocks, with very different growth characteristics that, in turn, control the growth of the whole plant. So, be sure to get the right rootstock so that the final tree fits into the place that you have for it. Also note that the rootstock only works when it has full control. If you plant the tree too deeply, the fruiting part will strike root, and its growth characteristics will take over. The graft union (pictured), should be about 12cm to 15cm above ground.
Most instruction manuals suggest that you should dig a generous measure of manure or compost into the planting hole, but I question this. If your dirt is good, it will make little difference. On the other hand, if you have a heavy, clay soil, the organic matter might rot away and leave you with a loosely planted tree. I think it is much better just to dig in a handful of bone-meal as a slow-release fertiliser, plant firmly, and improve the soil naturally as the tree grows by mulching from year two onwards.
Newly planted trees need support, but do not overdo it. A stout stake and a single tie-in point about a third of the way up is all that is needed. This allows the trunk to flex and strengthen while protecting the forming root structure from damage by excess wind. For trees on vigorous rootstocks, one or two years of staking is all that should be needed, but dwarf types need lifelong support.
For the first year in particular the tree will benefit from a bit of care. Water well during dry spells, and keep the weeds under control. Make sure that you don’t have mown grass right up to it, as this is about the most competitive surround possible. My trees have nothing more than a few daffodils within a metre or so of the trunk.