These cars are fairly heavy and basically the more rubber in contact with the road, the better. And 245 is about the widest you should put on the original 8" wide wheels; so you do need both wheels and tires if you want to go substantially wider than original.
A wider tire does have more rolling resistance so there could be a small loss of gas mileage, if that matters.
If you buy lightweight wheels, then the weight penalty for larger diameter wheels is very small, or could be a weight savings, like Old Goat already said.
To maintain your original overall gearing, keep the speedometer accurate, and have no change in acceleration (due to gearing) you want the same overall diameter tires as the original. for most Mustangs this is about 27.2"; you can check your exact original tires to find the tire diameter. Usually when people go from 18" to 19" wheel, the tire outer diameter stays the same, because they select a tire with lower sidewall to make the outer diameter the same as it was before.
Tire Rack is a great place to shop for wheels and tires. They have a tool that shows what the wheels will look like on your car. Their tool might be a little sticky about staying with the original wheel diameter; but I think you can force it to let you change the wheel diameter. They also have full tire specifications, including the overall diameter and the recommended wheel width.