The DI application requirements are a bit of a mystery with the recent updates, but, almost certainly, option 3. You need to take over a team that can immediately bring you to the NT. It will take at least a couple consecutive DII NT appearances (and winning a game) before you'll be eligible for any DI jobs.
I don't think prestige is the most important criteria for your purpose. Prestige moves quickly from season to season at DII, just like DIII. The far more important thing would be finding a DII team that will have returning players with some skillz & IQ. Most likely, that would be a high prestige team vacated during the job application period. However, if you look, you might find a sim-recruited superclass team (e.g. 9 returning juniors) that is only missing one transfer or JuCo player before being really good and bring you to the NT right away.
The key to moving up quickly to DI would be avoiding taking over a DII rebuilding project (no matter the prestige).