1) It is a Mitzvah for each Jew to personally take part in the building of their Sukkah, rather than have someone else build the entire thing for them. (See Talmud Kidushin 41a for the concept of Mitzvah Bo Yoser M’Beshelucho.)
One who does it himself receives more reward than simply asking or hiring someone else to do it. (Rashi ibid.)
This applies to all people, even respectable people, Talmidei Chachamim and dignitaries who usually should not be involved in menial tasks and physical labor. (See Machzik Bracha Siman 625:3. See also Talmud Shabbos 119a that Talmidei Chachamim toiling for a Mitzvah is their biggest honor. See also Mishna Berura Siman 250:4 and Biur Halacha Dibur Hamaschil Yishtadel.
The Steipler Zatzal was known to schlep the S’chach and place them on his Sukkah and refused to allow anyone to help him. This was also the custom of many other Gedolim.
2) If one is unable to build a Sukkah on their own and has someone else do it for them, it is proper to have the one building it to at least leave off a small amount of S’chach for the owner of the Sukkah to put up by himself. (Kaf HaChaim Siman 625:11)
Likewise, it is good to be personally involved in the set up and decorating of the Sukkah. (See Sefer Elef Hamagen Siman 626-644:4)
When one appoints someone else to build their Sukkah, it is proper to say to them ” You are my Shaliach Mitzvah, my messenger to do this Mitzvah of putting up my Sukkah and S’chach L’Shem Mitzvah, for the purpose and intent of performing the Mitzvah of sitting in the Sukkah” (Kaf HaChaim ibid.)
One should ideally not have his Sukkah built by a non-Jew, especially the laying of the S’chach. (Chida in Sefer Kaf Achas Siman 24:2. See also Elef Hamagen ibid.)
The Mitzvah of building a Sukkah is in it of itself a [part of the] Mitzvah and not only a means by which to be able to sit in the Sukkah.
Rav Reuven Margolis Zatzal in his Sefer Nefesh Chaya (Siman 625:1) writes that even one who cannot sit in the Sukkah (due to illness or other valid Halachic reason) and has no male family members that are required to sit in the Sukkah, still should have a Sukkah built to at least perform the mitzvah of “Building” a Sukkah! (As a proof to this ruling he cites the Talmud in Makos 8a and Shavuos 29a and also a Talmud Yerushalmi Brachos Perek 9:3 where the Talmud says to recite a blessing on the “Building of a Sukkah”.)
He goes so far as to say that this person would recite a “Shehechiyanu” when assisting in the building of this Sukkah as he won’t be reciting it when sitting in it!
Although we do not rule like the Nefesh Chaya in this matter, it still helps us understand the importance of being involved in the building of a Sukkah. (See Taz to Siman 641)