I've only recently started doing STFs, but here's what I've picked up so far:
1. Anti-protons seem to be the weapons of choice for the crit damage and since the borg appear to shrug off the procs of other weapons.
2. Resists to plasma damage in the shields, like the MACO shield, and perhaps armor. A BO with at least one copy of hazard emitters.
3. STO Academy has some walkthroughs on their site - http://www.stoacademy.com/walkthrough/stf/
Is there a guide or discussion somewhere on what the minimum bar for Elite STF is?
As mentioned earlier, the most critical part is KNOWING WHAT TO DO.
Then, you have to adapt your actions to the situation.
No 2 STF's work out quite the same.
On some runs you'll have experienced death machines OWNING the Borg but on others you'll be the one carrying the team. An STF Guide can be found here.
As for ships, the last "free" ships can be adequate (especially if you roll a KDF) but the Mirror ships can be had for cheap on the Exchange and are worth a test flight.
Rare (blue) Mk XI weapons/gear are sufficient but you don't want to be a scrooge over your deflector and shield so Very Rare (purple) Mk XII def/shield should be your first upgrade.
I use Mk XII positron deflector/covariant shield on my alts until I get around to unlocking KHG/Borg stuff.
Make sure one of the attributes are [PLA] on the shield.
I just wasn't certain if it was recommended a Fleet ship, seeing how they have a lot more hull than some of the others, if the C Store ships were secretly bad ships for the ESTF purpose or what.
I'm practicing during regular runs, get the understanding under my belt and my attack strategy. I only have trouble in one STF reliably and I think that's more a matter of tactical awareness than anything else.