It might be a good idea to do some combination of both of these choices. It is a good preparatory measure to budget how much you will spend on gas. You could determine the number of miles you will travel, and divide this by the estimated number of miles per gallon your car will get. This will tell you the approximate number of gallons of gas you will need. Then, you can multiply this number by the average price of gas during your trip. If you think the average price of gas is $1.75, you could instead use $2.00, to get a conservative number.
This will help you to budget how much you might need. However, on a road trip, you will need to drive the miles required to reach your destination, regardless of your budget. So in that sense, you should fill up as you go. You could keep track of your mileage as the trip progresses, to see if you are staying within the parameters you set (miles, miles per gallon, and gas price) in your budget, to make adjustments if necessary.
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