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Buying items other than clothing:
Until the nine days: It is permitted to buy all non-clothing items from the 17th of Tammuz until the start of the nine days. Seemingly, this applies even towards expensive items, and items that bring Simcha.[1] [Thus, it is permitted to purchase a car during this time.] However, some Poskim[2] rule one is to avoid purchasing all expensive items which give one joy and receive a blessing of Shehechiyanu, unless the matter is a necessity, or will cause one a monetary loss. According to Admur[3] however, we never recite a blessing on Shehechiyanu over purchasing new objects, even if they are very expensive, and hence one may purchase even such items up until the nine days.
During the nine days: It is permitted to purchase all inexpensive items during the nine days. However, expensive items may not be purchased unless it is an absolute necessity. See Chapter 3 Halacha 2 for the full details of this matter!
May one purchase house appliances and furniture, such as a fridge, washing machines, couch, during the three weeks?
If any of these items are a necessity, it may be purchased throughout the three weeks.[4] If the matter is not a necessity, it may be purchased up until the nine days. However, some Poskim[5] rule one is to avoid purchasing all expensive items which give one joy and receive a blessing of Shehechiyanu, throughout the three weeks.
May one purchase Sefarim during the nine days?[6]
Yes.
May one buy Tefillin during the three weeks?[7]
It is permitted to buy Tefillin throughout the three weeks.[8]
May one purchase a home during the three weeks?
One is not to do so unless it is an absolute necessity or a case of loss.[9]
May one purchase a car during the three weeks?
It is permitted to purchase a car for all purposes, up until the start of the nine days, as explained above. Some Poskim[10] however rule it is forbidden to buy a car for pleasure purposes during the three weeks.[11] If, however, one is buying it for purposes of making a livelihood, it is permitted to buy it during the three weeks.
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[1] See Admur Seder 12:5, as opposed to Luach 11:15 and 21, who rules Shehechiyanu is not recited over items that are not clothing, even if the vessels are made of gold and silver; See Igros Moshe 3:80 and Piskeiy Teshuvos 551:11 that if Shehechiyanu is not recited then it may be purchased.
[2] Igros Moshe 3:80; Piskeiy Teshuvos 551:11
[3] Admur Seder 12:5, as opposed to Luach 11:15 and 21,
[4] Igros Moshe 3:80
[5] Igros Moshe 3:80; Piskeiy Teshuvos 551:11
[6] Piskeiy Teshuvos 551:10; See Admur Seder 12:5 that we do not say Shehechiyanu over Sefarim
[7] Igros Moshe 3:80
[8] As Tefillin are needed only for the Mitzvah, and are hence not included within the prohibition.
[9] See Admur Seder 12:2 that Shehechiyanu is recited over purchasing a new home and hence its purchase is to be avoided during the three weeks.
[10] Igros Moshe 3:80
[11] The reason: As according to some opinions one needs to say Shehechiyanu on it. [ibid]