I've had a DR650 for dual sport touring. In a nutshell, you are looking at 30 yr old technology so the moto needs suspension and brake upgrades, maybe lowered seat, lowered foot peg mounts, Mikuni TM40 pumper carb, and oversized gas tank. About 2500 USD. For day rides you can skip most of these mods except for the suspension and brakes. Cogent DDC fork cartridges with stiffer springs is the minimum to upgrade the suspension. The rear shock has like zero damping so that should be upgraded also, but a Cogent shock ain't cheap. And yep carry a stator pick up coil in your tool kit. And fix the neutral switch before it fails. Don't forget bar risers, CR-Hi bars, and a headlight that works. Add another 500.
Taking all that into consideration, I've put about 40,000 miles each on two KLX400R (DRZ400E) modded dual sports, 25,000 miles on a modded XR650R dual sport, 40,000 miles on the Versys 650 modded with 19/17 wheel set, 10,000 miles on an XT250, and currently on a CRF250F dual sport plated.
If I lived in Texas, I would go with the DR650 for paved and mild dirt. Second choice would be the used DRZ400E because luggage is a problem. Forget riding two up on a DRZ for distance. Never been a fan of the DRZ S model with the CV carb. The Versys with a 17 wheel set is good if you stay on pavement, but off road it is a no go. Even with a 19/17 wheel set the handling is mediocre off road. The Versys was designed as a sport bike not a dual sport. The XT250 is good most roads for short tours but not so good two up. The issues with the 650R is again luggage for touring and forget two up, and no elec start for who did not get the kick start gene. If you crave adrenaline, then there is no substitute for the XR650R as it jumps to 100 mph.
Clean modded DR650s frequently come up for sale here and also on Advrider or DRRiders websites. Best of luck to you.