It is preferable to go to a Beit Knesset that is further away because there is reward for every step.
והאמר רבי יוחנן למדנו ... קיבול שכר מאלמנה ... קיבול שכר מאלמנה דההיא אלמנה דהואי בי כנישתא בשיבבותה כל יומא הות אתיא ומצלה בי מדרשיה דר' יוחנן אמר לה בתי לא בית הכנסת בשיבבותך אמרה ליה רבי ולא שכר פסיעות יש לי
Going to a further Beit Knesset.
ואם יש שתי בתי כנסיות בעיר טוב לילך להרחוקה כי שכר פסיעות יש:
Taking extra steps when entering the Beit Knesset.
(ב)
אמר הקב"ה: אם הלכת להתפלל בתוך בית הכנסת, אל תעמוד על הפתח החיצון להתפלל שם, אלא הוי מתכוון להיכנס דלת לפנים מדלת. ולמה כן? שהקב"ה מונה פסיעתך ונותן לך שכר.
(1) The law: If a Jewish person who passes before the ark [to lead the prayer], what is the law, should it be permitted for him to answer "Amen" after the [blessings of] the Kohanim? Such taught the sages: One who passes before the ark, he should not answer "Amen" after the Kohanim because of distraction. Our rabbis taught us: If he can answer without being distracted, he may answer. Why? Because nothing is greater before the Holy One, blessed be He, more than the "Amen" that the Jews answer. Rabbi Yehudah bar Simon: This "Amen" has three intentions. Oath, acceptance, faithfulness. How do we know "oath"? As its says, (Numbers 5:19-22) "The Kohen should put her under oath... and the woman is to say, Amen Amen."
The source for separation in the Beit Knesset.
מתני׳ מי שלא ראה שמחת בית השואבה לא ראה שמחה מימיו במוצאי יום טוב הראשון של חג ירדו לעזרת נשים ומתקנין שם תיקון גדול...
מאי תיקון גדול אמר רבי אלעזר כאותה ששנינו חלקה היתה בראשונה והקיפוה גזוזטרא והתקינו שיהו נשים יושבות מלמעלה ואנשים מלמטה תנו רבנן בראשונה היו נשים מבפנים ואנשים מבחוץ והיו באים לידי קלות ראש התקינו שיהו נשים יושבות מבחוץ ואנשים מבפנים ועדיין היו באין לידי קלות ראש התקינו שיהו נשים יושבות מלמעלה ואנשים מלמטה
The reason for the separation.
(יב) אַף עַל פִּי שֶׁכָּל הַמּוֹעֲדוֹת מִצְוָה לִשְׂמֹחַ בָּהֶן. בְּחַג הַסֻּכּוֹת הָיְתָה בַּמִּקְדָּשׁ יוֹם שִׂמְחָה יְתֵרָה שֶׁנֶּאֱמַר (ויקרא כג-מ) "וּשְׂמַחְתֶּם לִפְנֵי ה' אֱלֹקֵיכֶם שִׁבְעַת יָמִים". וְכֵיצַד הָיוּ עוֹשִׂין. עֶרֶב יוֹם טוֹב הָרִאשׁוֹן הָיוּ מְתַקְּנִין בַּמִּקְדָּשׁ מָקוֹם לַנָּשִׁים מִלְּמַעְלָה וְלָאֲנָשִׁים מִלְּמַטָּה כְּדֵי שֶׁלֹּא יִתְעָרְבוּ אֵלּוּ עִם אֵלּוּ.
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(11) [If] partners who bought a lulav or Etrog together, neither of them can fulfill the Mitzva on the first day until the other gives him his portion as a gift. [If] brothers bought multiple Etrogs [with money from a shared] estate and one [brother] took one [etrog] on the first day, he has fulfilled [his obligation]. However if they keep accounts [of the estate money] he has not fulfilled his obligation until the other [brother] gives it to him as a gift. And even if one bought an Etrog and the other a quince or one bought an etrog, a quince, and a pomegranate he has not discharged [his obligation] until the other [brother] gives him his share [in the fruit] even if he would not mind [under normal circumstances] if [the first brother] ate it.
(12) ...Although it is a Mitzvah to rejoice on all festivals, on the Sukkot holiday there was a time of overabundant joy in the Holy Temple, for it is written, "...you shall rejoice before the LORD your God for seven days." And how was this done? On the eve of the first holiday they would arrange in the Holy Temple a place for the women above and for the men below so that they might not mix one with the other. And they began to rejoice from the night after the first holiday, and continued on each and every day of the intercessory days of the holiday. They began after the Tamid offering was made in the evening to rejoice unto the rest of the day and through the night.
(13) ...And how was this joy [performed]? The flute was struck and the violin, harps, and cymbals, were played, and every person played any instrument he knew how to play. And those who knew to sing, sang. And they danced, and clapped their hands and thighs, and spun, and crowed, each according to their ability, and spoke words of praise and song. And this joy does not supercede the Sabbath or the Holy Day.
(14) It is an obligation to indulge in this merriment. This was not done by the folk of the land or whoever so wished, but by the greatest sages of Israel and the heads of the Yeshivot and the sanhedrin and the pious ones and the elders and the men of virtuous deeds, they were the ones who danced and clapped and played instruments and rejoiced during the days of Sukkot. But the entire People, the men and the women, all would come to look and to listen.
(15) The joy that a person should express in performing the Commandment[s] and in the love of God who commanded them, is a great worship [to God]. Whoever avoids expressing this joy is worthy of being punished for it, as it is stated: "...in return for you not worshipping the LORD your God with joy and with goodness of heart." And whoever carries hismelf haughtily and takes pride in himself and considers hismelf too dignified in such places is a sinner and a fool. Concerning this Solomon admonished and said: "Do not dignify yourself in front of a king." But whoever lowers himself and eases oneself in such places is the [real] great and dignified one who worships out of love. So did David, King of Israel, say: "...and I would be even less worthy than this and would be lowly in my own eyes." There is no greatness and honor but to rejoice before God, as it is stated: "And King David was spinning and crowing before God" etc. Finished are the laws of the Lulav, Praise to the Inspector of kidneys and heart
