You'll be hot and thirsty in the Florida heat and sun while visiting the parks. A cold bottle of soda, x 2 ppl, will be around $6. Two bottles, $12. You can get in line at a Counter service place and order a free cup of ice water, or use the water fountains around the park. It's your preference.
Since you'll have a car, there are two Hess gas stations on Buena Vista Drive in WDW. One is across from DTD (construction mess!), the other is across from Hollywood Studios. You can stop there and pick up drinks/water/snacks. Get a small, soft cooler to take drinks/snacks to the parks (it's allowed if non-alcoholic and non-glass). There's also a car wash at the Hess. I like to get the road trip dirt/bugs off my car. And gas price is good.
With the Dining Plan, you can order a large-size drink for no extra charge. There are a few park CS places with self-serve beverage stations (think: refills). Restaurantosaurus at AK, Electric Umbrella and Sunshine Seasons at EP, Tortuga Tavern and Be Our Guest Lunch at MK, Backlot Express at HS.
On your drive to/from WDW, you'll get fuel, but also food & drink. I love my Starbucks, so I have my trip mapped out with a stop there along the way. I think the iced latte I order helps keep me sharp when I'm driving.
I would have a $100-$150 budget for cold drinks, souvenirs, snacks. That's not much for 2 people for multiple days. You don't want to drive all the way to WDW, then deny yourself little things. The little things are part of what makes a Disney visit so fun!