Per reporting, Beshear, Cooper, Kelly, and Shapiro are in the running for VP.

Beshear is the safest pick, but also likely the least useful. If he was picked, a Democrat lieutenant governor would take his place till 2027.

Cooper is the second safest, and would help in North Carolina. He is term limited this year, so the winner of the 2024 gubernatorial election would be NC's governor regardless. The only wrinkle here is whenever he leaves the state to campaign the lieutenant governor is the acting governor per state law (that would be the crazy Republican Mark Robinson). However this isn't too relevant as Cooper leaves the state often and nothing really happens. Generally state provisions like this don't matter all that much. Since Robinson is running for governor this cycle maybe it will restrain him from abusing the position.

If it is Kelly, Democratic Governor Hobbs would appoint the successor. Kelly helps in a key state. A special election in 2026 would fill it. That's earlier than the end of his term in 2028. Appointed senators generally don't get an incumbency advantage. But the 2026 Senate map ain't too bad for Democrats compared to 2024.

Finally with Shapiro, the Democratic lieutenant governor would become governor till 2026. The Republican Senate president would become lieutenant governor and have the tie breaker vote in the legislature.