To which sons of Aharon is the Pasuk referring?
Rashi: It is referring to the offspring who will succeed him as Kohen Gadol.
What are the implications of the word "Yih'yu le'Banav Acharav"?
Yoma, 72b & 73a: It implies that the Kohen Gadol who comes after him (in Kedushah)
See Torah Temimah, note 18.
What does "le'Mashchah" mean?
Rashi, Ramban #1, Rashbam and Targum Yonasan: It means that wearing the Bigdei Kohen Gadol made the Kohen Gadol great. 1
Ramban #2: It means that Aharon who was anointed (with the anointing oil) would wear the Bigdei Kehunah Gedolah. 2
Targum Onkelos: It means that the Begadim enabled Aharon to purify the people.
As we find in Bamidbar 18:8 and in Tehilim, 105:15). The Ramban adds that it is a borrowed term that generally refers to the anointing of kings and Kohanim Gedolim, which elevates them to greatness - and he cites two examples from Melachim 1, 19, 15 & 16.
Moreover, the Ramban concludes, the Pesukim that Rashi quotes as proofs, also refer to anointing and not just to greatness (See Ramban, who elaborates).
What are the connotations of "u'Lemalei bam es Yadam"?
Rashi: It means that donning the eight Bigdei Kohen initiates a Kohen Hedyot into the Kehunah Gedolah. 1
Seforno: It means that future Kohanim Gedolim will be initiated by wearing the Bigdei Kehunah and will not be required to bring the Korbanos that Aharon and his sons brought for the Milu'im.
Such as in the era of the second Beis-ha'Mikdash, when there was no anointing oil.
What are the ramifications of the comparison of the anointing of the Kohen Gadol to his wearing the Bigdei Kehunah?
Yoma, 5a: It teaches us that (Lechatchilah) a Kohen Gadol had to have been anointed for seven days
See Gemara there that, Bedieved, even if he wore the Begadim for seven days and was anointed for only one, or vice-versa, sufficed. See also Torah Temimah, note 19..