Unless prepared to tackle the narrow roads, foreign language signs, and the traffic in Europe, I avoid driving. The alternative to driving is taking the train and/or bus. On the other hand, sometimes the best means of transportation is a car, and in that case, I do the following.
Renting and Insuring
I rent the car prior to leaving the US, I decline the insurance offered when initialing booking the rental (if permissible), and I purchase the insurance from the rental agency when I pick up the car. Car insurance is different in Europe than in the US, with the liability typically absorbed by the rental agency, although I always confirm this when renting. Which leaves collision damage waiver, a comprehensive/collision coverage called CDW, and theft insurance as my responsibility.
I purchase the best coverage, CDW zero waiver (zero deductible) and theft insurance from the rental agency. Which means, I would owe nothing in the event of vehicle damage or theft. And I have less stress to deal with.
If I am considering a credit card company or travel insurance for car rental coverage, I read the fine print. In the event of an accident, it might require repair payment upfront and then reimbursement through a claim.
Documentation for a claim would need to be accurate and complete. For example, if I don’t have a copy of the police report, the insurance company may reject the claim.
Details
The size of vehicle determines my rental cost. I choose the smallest vehicle without sacrificing comfort. Given narrow back roads and smaller parking spaces, a large vehicle would not be a good idea. Overall, European vehicles tend to be smaller.
Manual transmissions are popular in Europe, with automatic transmissions typically costing more to rent. Also lane directions and driver sides are reverse in some countries. Therefore, if I am driving in the UK, I always rent automatic transmissions. Electric vehicles are also available to rent. And fuel (petrol) is usually diesel and measured in liters with fuel stations not so abundantly available.
I don’t rush into the rental decision, but I research the available vehicles using different rental sources. There are fees and taxes, such as returning the rental in a different city or country, which can be costly. I pay attention to the full and final quoted price.
I expect highway tolls in Europe. Payment may be made in cash or through an aerial monitoring system using a credit card. Sometimes a highway travel permit is required that I can purchase from a fuel station or the rental agency. I always inquire at the time of car pick up.
Some countries do require international driving permits. Which means, I purchase a permit from AAA that is good for one year and cost about $35. I may never need to present the permit, however, if involved in an auto incident, I really should have one.
A parting thought on car rental … I don’t leave obvious physical articles in the vehicle that is a clear indicator I am a tourist. It may draw unwanted attention.