A clunker would be fine in certain situations. However, for me, I prefer to have a relatively newer vehicle that is dependable and has minimal mechanical issues. I don't believe that there's anything worse than having a vehicle that you can't depend on, especially if you do a lot of long distance traveling. Search for low mileage vehicles that are a year or two old that have good maintenance records. Check Consumer Report or other sources that compile maintenance data. Yeah, buying am older vehicle may eliminate a monthly car payment, but those occasional repair issues can be costly and surprising, and it may be difficult to budget for those unexpected repairs. Certain brands and models offer lifetime/unlimited mileage warranties on the engine and drivetrain of their vehicles, that can be a good choice, but read the exclusions/limitations carefully.
Many States don't tax vehicles on an annual basis, so it's not an issue for many folks. An annual tax on vehicles means the government ultimately owns the vehicle. The vehicle owners pay a rental fee to the government for the privilege of driving that vehicle. And the owners maintain the vehicle for the government too. Nice set up!
Oh yeah, as a second vehicle, you might consider a motorcycle with a sidecar. Ural motorcycles can be driven in the snow, due to a unique two wheel drive system. They are very easy to maintain, as they're very simple, based upon a WW II BMW design. Insurance and fuel costs are cheap too!