Get a Weber or forget it
With all due respect to fellow Cheftalkers, I submit that trying to make "Texas style barbecue beef ribs" on a gas grill would only be an exercise in frustration. I've been there, and have gone on to 5+ years of BBQ success.
To clarify: You can *cook* the ribs on a gas grill, but you can't make *barbecue* on it. In my opinion.
Barbecuing requires low, slow cooking, with steady heat. I use 6 hrs at about 250 F for pork ribs. It's the "low and slow" heat over time that breaks down the connective tissue and turns gnarly cuts into tender, moist ribs. No gas grill I've seen can supply that without temperature dips and spikes - they're far too well ventilated.
The good news, as CC pointed out, is that a charcoal Weber-type kettle grill can deliver. See this primer: http://bbq.netrelief.com/Tips/weberribs.asp
Oak and hickory are the typical smoke woods but most hardwoods can stand in, in a pinch (I've used maple), and some people prefer fruitwoods such as apple or pear. By all means use a rub - any mix of powdered spices you like. I use salt, garlic powder, black pepper, brown sugar, ground chile, and cumin, for starters.
As for the mop, lots of people use a spray bottle. Another popular mop liquid is half cider vinegar, half apple juice.
If all you will have is a gas grill, I've got two suggestions.
1. skip the BBQ idea and go with a grilled spare rib, though I've only grilled pork and don't know how beef ribs do grilled. I've wowed crowds with my Vietnamese marinated grilled pork spare rib, though. (Shallots, garlic, fish sauce, brown sugar, black pepper, and toasted tomato paste, marinate overnight).
2. you could try approximating the BBQ effect by roasting the ribs in a 250 F oven for 3-4 hours and then grill them with soaked wood on a burner for smoke. You'd get some tenderness and some smoke, but it will only be a substitute.
My problem always was that after the amazing BBQ I had other places, I'd be trying to duplicate the wonder, I'd do all the work, but use impossible equipment or techniques, and then while I was eating I'd only be reminded of what it wasn't.
But then, I'm a Q freak.