On our way to Crystal River, FL from SW Michigan we always take 231 through Dothan and continue on 231 all the way to I-10. In fact, we go right past Anderson, IN along I-69 on our way. I think this route is a bit faster because you're doing I-10 east/west with no stop lights. I will admit that Dothan is a slowdown though.
If you need a nice overnight campsite along the way I'd like to suggest Deer Run RV Park north of Troy, AL. It's inexpensive, paved pads, FHUs, cable TV for under $30/night. Good Sam will save a few dollars too. We often stay here going north and south.
http://www.deerrunrvpark.com/US-19 is a very good 4-lane road south of I-10. And johnhicks is correct, don't stay on US-19 south of US-98 (too many lights/traffic). Definitely pick up the Suncoast Parkway/589 shortly after getting on US-98. It'll take you right into Tampa.
2018 Chevy 2500HD Duramax - 2015 Cedar Creek Silverback 29RE
16K Huskey EZ Roller Hitch - EU2000i Honda Generator