Democratic Primaries

To choose for an assistant president and friend, capable of handling a big, important portfolio. The role he filled for President Obama.

This isn't the same as "can he/she step right in and govern" -- traditionally "right in" only after succeeding to the presidency. Biden wants his VP to actually step right in and "govern" with him under his authority, again as he did as Obama's workmate.

Unlike the thinking of many posters, I'd move political campaign considerations down in priority. Not that they aren't important, but Biden is well known and liked nationally, and is probably as reassuring to potential conservative-leaning swing voters as any Democrat could be. It very quickly becomes 90% about the presidential candidate and HIS or HER coattails anyway, and in order to get a great assistant president I'm guessing he could choose a running mate who satisfied the political considerations of getting elected relatively weakly.

Electing our first woman VP (Democrat of course!) will be a very significant step forward in itself. What I can imagine is Biden naming some of his cabinet appointees fairly early in the GE, and those would also be used to meet expectations of moving people from various groups and geographic locations into power.