Can anyone recommend the fastest way to get from Jacksonville to Naples, FL. Should I take I4 and I75

That is the way to go. I-95 S to I-4 W to I-75 S. I-4 is heavily congested from Daytona to Tampa with heavy construction much of they way so be sure to time it right. I-4 is backed up from around 6am to 8pm in Metro Orlando every day.

That's why I asked the question. I wonder if any local residents have a better route. Thanks.

There are a few other ways I have taken. They may be a little longer but they are more interesting. You can take I-95S to I-4W to Haines City/US27 and get onto US17 S and take that to I-75 S in Port Charlotte. This will save you some miles but the road goes through a few small towns where you'll have to slow down. It does keep you out of the Tampa Bay area which can be heavily congested. You could also head west on I-10 from JAX and get on US301 S to Archer Rd (SR 24) in Gainesville and take that to I-75 S. This would allow you to skip Orlando's traffic. Gainesville's Archer Rd backs up pretty bad in the afternoon so try an avoid that if you go that way.

How about I-95 down to Ft. Lauderdale and then I-75 west to Naples?

You could do that. I drive all over the state every day with my job. I did that last week but it is a longer ride. Naples is at the same longitude as Jacksonville so by going southeast down to Ft Lauderdale then getting on the Sawgrass Expressway South (SR 869) to I-75 N going west across Alligator Alley is alot longer. If you are aren't in a hurry you might enjoy it. You will see pretty much the whole state. You could stop in West Palm or Ft Lauderdale and along Alligator Alley there are some rest areas right in the middle of the Everglades. If you go that way and it is near rush hour as you approach South Florida, it is a good idea to get on the Turnpike in Ft Pierce at Okeechobee Rd (SR 70) and take that south. It parallels I-95 and is not as congested and does not back up unless there is a wreck.

I 95 south to SR 70 west (near Ft Pierce) to Us 441 south to SR 76 west to Us 27 west to Sr 78 west to Sr 29 south to Sr 80 west to I 75 south to Naples. This is a good route when traffic is light ie nights or early am and shorter in miles. Also you can see Lake Okeechobee , sugar cane and a winery ( free tour ) on SR 80.