shabbat - What is technically required for shalosh seudas?

To meet the minimum halachic requirements for the mitzvah of shalosh seudas on Shabbos or Yom Tov, must you have:

(1) Bread? (I see discussion of lechem mishneh here. Must a k'zayis be eaten by each person? ...A k'beitzah? [Or is it a k'beitzah of total food in the meal?]) --See also the question premise here, which implies you don't need bread at shalosh seudos

(1b) If not bread, mezonos? How much?

(2) Meat?

(3) Cooked food?

Related:

Lechem Mishneh by the Third Shabbos Meal

Answer

You should use bread. That is the minimum Halakhic requirement. If you for some reason really, really can't have bread (eg. allergy, availability, repulsion), might as well satisfy some minority opinions in Rishonim who permit using other foods.

Shulchan Arukh OC 291:5

צָרִיךְ לַעֲשׂוֹתָהּ בְּפַת; וְיֵשׁ אוֹמְרִים שֶׁיָּכוֹל לַעֲשׂוֹתָהּ בְּכָל מַאֲכָל הֶעָשׂוּי מֵאֶחָד מֵחֲמֵשֶׁת מִינֵי דָּגָן; וְיֵשׁ אוֹמְרִים שֶׁיָּכוֹל לַעֲשׂוֹתָהּ בִּדְבָרִים שֶׁמְּלַפְּתִים בָּהֶם הַפַּת כְּבָשָׂר וְדָגִים, אֲבָל לֹא בְּפֵרוֹת; וְיֵשׁ אוֹמְרִים דַּאֲפִלּוּ בְּפֵרוֹת יָכוֹל לַעֲשׂוֹתָהּ. וּסְבָרָא רִאשׁוֹנָה עִקָּר, שֶׁצָּרִיךְ לַעֲשׂוֹתָהּ בְּפַת אֶלָּא אִם כֵּן הוּא שָׂבֵעַ בְּיוֹתֵר.‏
You must make it with bread. And some say you can make it with any food made from the five species of grain; and some say you can make it with things that accompany bread like meat and fish, but not fruit; and some you can make it even with fruit. And the first opinion is primary, that you have to make it with bread, unless you are [already] exceedingly full. (all translations mine)

Indeed if you are exceedingly full, you are exempt (ibid. :1):

יְהֵא זָהִיר מְאֹד לְקַיֵּם סְעֻדָּה שְׁלִישִׁית, וְאַף אִם הוּא שָׂבֵעַ יָכוֹל לְקַיֵּם אוֹתָהּ בְּכַבֵּיצָה, וְאִם אִי אֶפְשָׁר לוֹ כְּלָל לֶאֱכֹל אֵינוֹ חַיָּב לְצַעֵר אֶת עַצְמוֹ. וְהֶחָכָם עֵינָיו בְּרֹאשׁוֹ (קֹהֶלֶת ב, יד) שֶׁלֹּא יְמַלֵּא בִּטְנוֹ בִּסְעֻדַּת הַבֹּקֶר, כְּדֵי לִתֵּן מָקוֹם לִסְעֻדָּה שְׁלִישִׁית.‏
One should be very careful to fulfill the third meal, and even if he is full he can fulfill it with an egg's bulk [some (MB) say an olive's bulk is sufficient -- AA], and if he can't eat at all he is not obligate to pain himself. But the wise one looks ahead and doesn't fill his belly at the morning meal in order to give space for the third meal.

Of course, if people know about the option of leniency and they have a nice delicious morning meal in front of them, not everyone will behave so wisely...

The Shulchan Arukh haRav writes (ibid. :7):

ואין לסמוך כלל על כל זה אלא אם כן אי אפשר כלל בענין אחר כגון שהוא שבע ביותר ואי אפשר לו לאכול פת בלא שיצער את עצמו
And one should not rely on [the lenient opinions] at all unless it is impossible any other way, such as he is exceedingly satiated and he cannot eat bread without paining himself [at which point he is exempt].

The Chayei Adam writes (Shabbat 7:3):

ומי שא"א לא כלל לאכול כזית פת בסעודה ג' בשעת הדחק יש לסמוך לצאת במיני מזונות לפחות בבשר ודגים ואם אין לו כל זה עכ"פ יאכל פירות אבל כ"א חייב לדחוק עצמו לאכול עכ"פ כזית פת
And one who is unable at all to eat an olive's bulk of bread at the third meal in a Sha'at HaDechak should rely to fulfill his obligation with Mezonot with meat and fish, and if he doesn't have all that at the very least he should eat some fruit, but every person is obligated to push himself to eat at the very least an olive's bulk of bread.

The Arukh haShulchan writes (OC 291:12) about those who are regularly lenient to not use bread:

והנה גם דעת בעלי הש"ע דהעיקר לדינא שצריך פת, וכיון שדעת הרי"ף והרמב"ם והרא"ש והטור והש"ע שצריך דווקא פת - חלילה להקל בזה, ועבירה גדולה ביד המקילים בזה לצאת במיני תרגימא. ויש להזהיר על זה מאד מאד, ואין היתר כי אם לחולה, והמזלזלים בסעודה שלישית לצאת ידי חובתם בלא פת - עתידים ליתן את הדין.‏
And behold, the authors of the Shulchan Arukh are of the opinion that the primary position is that bread is needed, and since that is the opinion of the Rif, Rambam, Rosh, Tur, and Shulchan Arukh that bread specifically is needed, [God] forbid to be lenient on this, and it is a big sin in the hands of those who are lenient to eat other foods. And one should be careful about this very, very much, and there is no leniency other than to one who is ill, and those who disgrace the third meal by fulfilling their obligation without bread will eventually be dealt justice.