It sounds like a great offer; were I unemployed, I would probably jump on it. As for miles on the Z, even within a 20 mile radius, you may find yourself exceeding 100 miles/day, so the miles will add up.
The IRS sets a mileage reimbursement rate and adjusts it periodically. This rate is intended to cover the costs of using your car for business: gas, insurance, normal maintenance, wear and tear, and depreciation. If you are not being reimbursed for your mileage at the Federal rate, you can take a deduction on your taxes.
Record all business-related mileage. I used to use my trip odometer. Zero it at the beginning of the trip and note the total miles at the end of the day; travel to meals is included. If you are working from home, you must deduct commute mileage. Ask your employer what their standard is (usually not more than 10 miles one way) or consult with your tax preparer. If you work from your employer's premises, you don't need to deduct the commute. I used a simple vertical spreadsheet to record the actual miles traveled, automatically deduct the commute and calculate the claimed miles and reimbursement.
Record the amount reimbursed by your employer from your expense checks or pay statements.
At the end of the year, provide this information to your tax preparer. The deduction can be substantial. I drove over 52k miles in the 2007 tax year and this was my second-largest deduction, behind home mortgage interest.
If you find yourself putting more miles on the Z than you intend, you might consider leasing a car. A good part of this (but possibly not all) will also be deductible on your taxes; in this case an economical vehicle will be to your financial advantage.
Edit: If you want a copy of the spreadsheet I used or have other questions, send me a message and I'll do my best. But your tax preparer may be a better choice. ;)