Be careful about deciding. Whilst it may be tempting to travel the country & have fuel expenses paid, you may be expected to travel down to Cornwall on Monday, be there for 9, finish at 5 then be expected to travel to Glasgow on Tuesday, again, 9 - 5... OK, them's extremes, but it could happen. Also, bear in mind all those extra miles you're putting on your car - will impact on your insurance and affect resale value (mileage allowances rarely reflect true running costs).
Will you be expected to travel hundreds of miles between branches? and what about timescale? remember speed limits etc. the higher the mileage, the higher the chances of being pulled if you are speeding.
As with option 2, if they provide the car etc, then all well and good but will you be fit for work after driving 75miles in heavy traffic?
And what are you going to be like after driving home? (this also effectively increases your working day.)
Just remembered, we had some people in a few months back, giving additional training to all our drivers. They'd travelled from Wales that morning, stayed overnight in local B&B, worked the next few days with us, staying in B&B then up to Manchester for a couple of days, Wales for the Weekend then up to tour Scotland the following week.
I thought they should have retired years ago, turned out they were in their early 40s.