Gemara

R. Shimon learns from "from wine and strong drink Yazir (he will vow to abstain)" that a Nazir is forbidden wine of a Mitzvah, just like regular wine.

Suggestion: 'Wine of a Mitzvah' is wine of Kidush and Havdalah.

Rejection: (This cannot be.) One is bound (to drink it) by an oath (from Har Sinai)!

(Rava): Rather, he swore that he would drink wine, then accepted Nezirus. The Nezirus takes effect and he is forbidden to drink wine.

Pesachim 106a (Beraisa): "Zachor Es Yom ha'Shabbos Lekadsho" - one should be Zocher (mention) Shabbos (i.e. say Kidush) over wine.

106b ( Rav Yitzchak bar Shmuel): When Rav preferred bread (he was hungry), he said Kidush on bread. When he preferred wine, he said Kidush on wine.

107a: Ameimar visited the locale of Rav Chisda's sons. They did not have wine, so they offered to him beer for Havdalah. He declined, and did not eat until obtaining wine the next day. The next time he visited they again offered him beer for Havdalah. He concluded that beer is Chemar Medinah (an esteemed drink in the locale used in place of wine, for wine is scarce), and made Havdalah on it.

(Rav and Shmuel): Just like one may not make Kidush on beer, one may not make Havdalah on it.

Levi sent to Rebbi a very tasty date beer. Rebbi said that it is fit to make Kidush on it. At night he had pain (diarrhea).

(Rava): One who makes Kidush on beer should (be punished with poverty and) have only beer to drink.

Rav Huna saw Rav Mekadesh on beer. He suggested 'Did you start to profit through beer (and therefore you prefer it?)'

(Beraisa): One may say Kidush only on wine. One blesses (Birkas ha'Mazon) only over wine.

(Beraisa): One may not make Kidush on beer;

R. Elazar b'Rebbi Shimon permits.

Rishonim

Question: Since Nezirus forbids wine that is not a Mitzvah, it also forbids wine of a Mitzvah! Why did the Gemara say that Nezirus does not forbid wine of Kidush and Havdalah, due to the oath from Sinai?! All the more so this is difficult for Rava, who answered that he swore to drink wine, then accepted Nezirus!

Answer (Tosfos Nazir 4a DH Mai): R. Tam says that the text should say (incredulously) 'is one bound by an oath (about these)?' Even though Kidush is mid'Oraisa, the obligation to say it over wine is not.

Rebuttal #1 (Ra'avan Sof Teshuvos, DH Hiksheh): Our text is correct. A Neder or Nezirus forbids Mitzvos only if one specified!

Rebuttal #2 (Or Zaru'a 2 Shabbos 25): If one swore to drink wine, Nezirus forbids wine because he can permit his oath. Nezirus does not take effect on wine of Kidush and Havdalah, for the oath of Sinai cannot be permitted.

Rif (Pesachim 22a): One may say Kidush and Birkas ha'Mazon only over wine. Beer may not be used, unless it was the main drink of his meal.

Ran (DH Ein): If it was the main beverage of his meal it may be used for Birkas ha'Mazon, but not for Kidush.

Rambam (Hilchos Shabbos 29:17): In a place where beer is the (standard beverage, in place of) wine, it may be used for Havdalah, but not for Kidush.

Source (Hagahos Maimoniyos 4): Even though Rav and Shmuel forbid beer for Havdalah, the Halachah follows the latter Amora'im, i.e. Ameimar and Rav Ashi. (Rav Ashi heard the episode with Ameimar and agreed with it).

Magid Mishnah: Some Ge'onim permit Kidush on beer where it is Chemar Medinah. Others forbid, for bread may be used.

Rosh (10:17 DH Omru): One may not make Havdalah on water even in a place where there is neither wine nor beer. Some say that the Heter to use Chemar Medinah is when wine (grapes) is not grown within one day's journey of the city.

Suggestion: One may not make Kidush on beer even if it is Chemar Medinah. We learn from Rav Chisda. (The Rashbam says that Rav Chisda forbids in this case!)

Rejection (Rosh 10:17 DH Boi): The Rashbam agrees that the Halachah is unlike Rav Chisda regarding Havdalah. Perhaps it is unlike him also regarding Kidush! It is better to explain that Rav Chisda allows beer when it is Chemar Medinah. If so, he does not argue with Ameimar. Also the Yerushalmi disqualifies beer for Kidush, but perhaps this is only when it is not Chemar Medinah.

Suggestion: When Motza'ei Shabbos is Yom Tov, and Kidush and Havdalah are done together, surely we do not say half (i.e. Kidush) on bread and half (Havdalah) on beer (where beer is Chemar Medinah). This suggests that beer may be used for Kidush!

Rejection: Rav Amram Ga'on says that when Kidush is on bread and it is together with Havdalah, also Havdalah may be on bread. Presumably, Rav Amram never allows Kidush on beer. However, most Ge'onim allow Kidush on beer where beer is Chemar Medinah. It is preferable to say both on beer than on bread, for Havdalah by itself cannot be on bread.

Rosh (ibid.): Ri and Ra'avan permit Kidush on beer where it is Chemar Medinah. However, at night, when one may make Kidush on bread, this is better, for the meal (which is based on bread) is to honor Shabbos. The day Kidush cannot be on bread, for then there would be no extra Berachah!

Poskim

Shulchan Aruch (272:9). When wine is scarce, some permit Kidush on beer and other beverages, and some forbids. The Rosh does not allow Kidush on beer at night, for Kidush may be said on bread. For the day Kidush he permits on beer, so that there will be an extra Berachah before ha'Motzi.

Beis Yosef (DH v'Chosuv): If wine is available, even if it is expensive, one must use it for Kidush and Havdalah. Chemar Medinah may be used if Kosher wine is scarce now, even if wine is abundant in most years and wine of Nochrim is available.

Taz (6): If wine is expensive one need not use it for the day Kidush, which is less obligatory than the night Kidush. Even great people in our locale do not make Kidush on wine during the day, although the ideal Mitzvah is with wine.

Rema: Our custom is like the Rosh. One should not make Kidush on bread if there is wine in the city.

Magen Avraham (8): When possible we avoid Kidush on bread because R. Tam (Tosfos 106b DH Mekadesh) does not allow this.

Mishnah Berurah (31): Even the Poskim who argue with R. Tam allow Kidush on bread only when there is no wine, or if the person prefers bread to wine. Perhaps people are lenient today because they prefer bread.

Kaf ha'Chayim (49): Chemar Medinah such as whiskey may be used only if one can drink a Shi'ur (Malei Lugmav) without pausing. B'Di'eved or in pressed circumstances, we may join the amount drunk by others.

Shulchan Aruch (296:2): One may not make Havdalah on bread, but Chemar Medinah or other beverages may be used, except for water.

Beis Yosef (DH v'Chosav): Bread is relevant to Kidush, for Kidush must be b'Makom Seudah, but it has no connection to Havdalah.

Mishnah Berurah (8): When wine is available it should be used. One who makes or hears Havdalah on wine is called Kadosh and a treasure - "vi'Hyisem Li Segulah...;...v'Goy Kadosh...; Va'Avdil".

Kaf ha'Chayim (21): If after Havdalah one found that the 'wine' was really vinegar, the Chida requires repeating Havdalah. However, the Tur brings an opinion that Havdalah does not require a cup. This is a Safek Berachah mid'Rabanan (even if Havdalah is mid'Oraisa, mid'Oraisa one is Yotzei without a cup), therefore it is better not to repeat Havdalah.

Note: If one can hear Havdalah from someone else this would be best. Many say that the Tur's 'lenient opinion' was based on a mistaken text.

Rema: It is better to make Havdalah on a Pagum cup of wine (from which someone drank) than on beer. Our custom is to make Havdalah on (barley) beer (which is Chametz) on Motza'ei Pesach because (then) it is dearer than wine.

Magen Avraham (6): This is only where beer is Chemar Medinah, but not in Eretz Ashkenaz, especially since wine is available.

Taz (3): Even on Motza'ei Pesach, if one prefers wine, he should make Havdalah on wine.

Kaf ha'Chayim (24): Pagum wine is better for Havdalah than beer. Wine counters the Midah of Din, which begins its dominion on Motza'ei Shabbos. If the wine is not fully diluted, the Pegam should be fixed with a drop of water.

Shulchan Aruch (ibid.): Some say that when Motza'ei Shabbos is Yom Tov, since Kidush may be on bread, also the Havdalah may be on bread.

Source #1: A Mishnah (Berachos 51b) discusses the order of the Berachos of light, spices, Mazon and Havdalah. Surely, 'Mazon' cannot refer to Birkas ha'Mazon, for one may not eat before Havdalah! Rather, it refers to ha'Motzi. The Mishnah discusses Motza'ei Shabbos, and permits Havdalah on bread.

Rebuttal (Rif Berachos Sof 38b): The Mishnah discusses Birkas ha'Mazon (Tosefta). The person was eating when Shabbos ended (Yerushalmi).

Source #2 (Gra): Eruv Chatzeros should be with bread, and Shituf Mavo'os should be with wine. Since bread is appropriate for the Eruv, we may rely in it for the Shituf (Rashi Eruvin Sof 71b. The same principle applies here.)

Shulchan Aruch (ibid.) Others say that it is better to say both Kidush and Havdalah on beer.

Kaf ha'Chayim (27): Whenever the Shulchan Aruch says 'some say...and others say', he favors the latter opinion.

Gra: This is like the opinion (272:9) that it is better to make Kidush ha'Yom on beer than on bread.

Rema: The former (some texts - latter) opinion is primary. (Poskim argue about the correct text of the Rema. The Gra's text surely said 'former', for the Rema (272:9) says that it is better to make Kidush on bread.)

Mishnah Berurah (15): One should strive to get wine, for many do not allow Havdalah on bread even on Yom Tov.