Best way fastest from Florence to Teramo?

Probably train
Have you looked at schedules?

https://www.trenitalia.com/content/tcom/en.html

How many? Like you would need a van or?
How will you get around when you get there? A private driver would be exorbitant.
See schedules at https://www.trenitalia.com/en.html

Is this the large family of 10-16 you posted about last summer? If so, would the elderly members be able to manage train travel (with your help? The train is going to require changes, and will take all day (8 ish hours). And you need to decide how you will get around once you get there.

A private driver and vehicle would require a bus, and would be exorbitantly expensive.

Self drive would require multiple drivers and vehicles, each with an International Driver's Permit.

Personally, I'd go with self drive, but you need to discuss this with your group.

Yes. Family of 10ish..Is it better to travel from Venice to Teramo?
Or Rome to Teramo?
and Italy doesn’t use Ubers? Or taxis? What’s the app?

Information about taxis, apps and Uber can be found on this forum
Use the search function
Filter by Type and Date

Check Trenitalia as linked above to determine the best route to travel

Family of 10ish..Is it better to travel from Venice to Teramo?
Or Rome to Teramo?

You seem to be literally all over the map here. Where are you going to be before going to Teramo? And where are you going afterwards? Plug that into Google Maps and get a rough idea of driving times or public transport options.

If there are 9 or more of you, you need a mini bus driven by someone with a bus license. Teramo is about 3 hours by bus from Rome or maybe 5 by train. Florence is farther. You will need about 6 hours by train. Venice is much farther north.