The Shulhan Aruch (O.H. 551:2) says that as of Rosh Hodesh Av, any joyful business deailngs are forbidden. Examples of joyous dealings include those whose purpose is to expand a business or increase profit. The Mishna Berura (O.H. 551:11) includes the purchase of items needed for a wedding as joyful transactions and says that those are also forbidden.
The custom is to be lenient and permit, however, business that is meant to sustain the status quo.
Regarding purchasing a car, Rabbi Moshe Feinstein (Igrot Moshe, vol. III , 80) writes that if the car is for pleasure and one would recite “Sheheheyanu” on it, then it would be forbidden during the entire Three Weeks and all the more so during the Nine Days. However, if the car will serve a vital function, like providing transportation to work, then it would be permitted to buy it. In a similar vein, the Kovetz Halachot (ch. 12, § 14 ) writes that one may purchase furniture or appliances which are necessary for the proper functioning of a home, as long as they are not bought for expanding or renewing one’s home. Thus if one’s washing machine breaks down, for example, one would be able to replace it during the Nine Days. Furthermore, Rabbi Shaul Israeli (Nehamat Israel, ch. 10, comment 13), citing Rabbi Nissim Karelitz, says that silverware and other small home purchases are permitted. Rabbi Ovadia Yosef (Hazon Ovadia, pg. 168) concurs with these views.
According to the Kovetz Halachot (ibid:comment 18) one is permitted to order items online during the Nine Days if they are scheduled to arrive after Tisha Be’Av, since one will not have the opportunity to deal with, much less enjoy them. Even if the arrive during the Nine Days, if one were to set them aside, it appears that this would be permitted. Similarly, if one purchases items but never actually deals with them, such as if one sells at a later time, this would be permitted.
Summary: Purchases or business deals that involved in expanding a business or a home are not permitted during the Nine Days. Purchases that are vital to the functioning of one’s home are permitted. Online ordering is permitted if the item will arrive after the Nine Days or if they will be set aside till that time.