To which sons of Aharon is the Pasuk referring?
Rashi: It is referring to the son who succeeds him as Kohen Gadol.
What does "l'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: The Pasuk means that Aharon who anointed (with the anointing oil) would wear the Bigdei 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 consecrates a Kohen Hedyot into the Kehunah Gedolah. 1
Seforno: It means that future Kohanim Gedolim 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.