It might be easier to buy a second-hand car to begin with, but always shop around, as prices for used cars can be more expensive than in the UK.
If it’s definately a new car you need or want, then there are usually finance options available through most dealers, though it may be more difficult to get set up, even once you’ve got your NIE, bank account, address, etc… That said, the car industry throughout Europe is crying out for people to buy new vehicles, so it may be a good idea once you’re there to shope around a few dealers and see what deals and options they will offer you. Finance companies can and often will search for your credit history back in the UK, so as long as there’s no previous problems, you should be ok.
As for the delivery time on a new vehicle, this can vary widely. My parents had to wait for nearly 2 months for their new Nissan X-Trail from the main dealer in Granada. They were given the usual “15 days” by the salesman. As with any large purchases here though, you just need to be patient. Customer service generally isn’t of a similar standard or importance as in the UK or USA perhaps, though your consumer rights are pretty much the same.
Good luck
Heath