This was my first year grafting also. I grafted apple and pear trees mostly.
I had really good success with putting them in a raised nursery bed that had healthy and well draining soil, with a
fence around it to keep out the critters.
I grafted the trees about a month and a half before our estimated last forst date, and I planted the trees outside right after I grafted them. I think it got down to about 20 degrees F a few times and the trees were fine.
Planting them in their final location after being grafted would be ideal in my opinion if possible, but I wanted to just use the the rootstock temporarily, and remove it before I planted them in their final location so that they would be growing on their own roots. Planting them in their final location could also save a lot of time and work too, since instead of having to be planted twice, they would only have to be planted once. It would probably also result in a healthier and faster growing tree since it would only go through transplant shock once, and then be in its final home after that. The majority of my grafted trees have grown very vigorously so far, better than a lot of the year old trees that I've bought. I think a key to planting them in their permanent spot, would be to have the location already prepared for them with soil that drains easily and is not waterlogged, and creating soil that is full of organic matter from mulching with leaves, branches, logs, and other plant debris, which can help provide the right nutrients and encourage beneficial fungi that will greatly help the tree's immune system!
I planted them in a nursery bed instead of their final home because I wanted to just use the the rootstock temporarily, and remove it before I planted them in their final location so that they would be growing on their own roots, and I didn't have
enough time to plant them all in their final location at the time, and I didnt have a spot picked out for them yet and prepared for them, and the soil was healthier in the nursery bed.
It will probably depend on what your goals are for the plants, as to which way may be best for them.
I will probably use the nursery bed for grafted trees in the future so that I can remove the rootstock, but for air layered or propagated plants on their own roots, I hope to be able to plant them in their final home in the future if it is possible.
I really enjoyed grafting this year for the first time and really felt like it was a really great experience!