Hi Kristi,
What I'm telling you I know is true for apples and roses, and since plums are in the same family(quince and peach are too,) I assume it is true for them as well. The seed should be kept moist and sown outdoors because they need winter to break dormancy. Winter sowing works well.
The tree that grows will not be the same as the tree it came from, but it could be very nice. To get the same variety, you need to root or graft a cutting.

For citrus the seed need to be kept moist if not sown immediately. Of course they don't need cold to germinate. Some citrus like Key Limes will come true from seed. The seeds if removed from the lime and put in a moist paper towel in a baggie will start to sprout in just a few days.
Remy