I've been in this situation and previously had a company car.
When I recieved an allowance I had the same options as you.
Get a new vehicle, get something on a persoanl lease or buy used.
I bought a low mileage used Volvo S60 – suited my needs as I'd be doing big miles. I'd have paid through the nose on any sort of lease/contract because of the mileage and I didn't want to spend all my allowance on a depreciating asset.
You'll be taxed on your allowance but your company should allow you to reclaim fuel or cover your fuel costs.
It'd be unusual for them to allow this at maximum HMRC levels of 40p per mile for the first 10,000 then 25p for every mile after that. These rates are usually for those who don't receive an allowance.
My only advice would be that you need to consider the amount you'd actually get after tax and all the servicing costs of the car, insurance & tax.
My motivation for getting a second hand car was to maximise the allowance I was getting (spend it on bike gear), I'd rather have it in my pocket then have a newer shiny car on the drive. I considered the car a tool of the job.
HTH