You have to ask yourself what you actually want. Do you want to outright own your car? Or do you want a brand new car every couple of years? If you want a new car every couple years then the way to go would be lease, provided you don't do a whole lot of driving. They usually have about a 12,000 mile per year limit on the lease and anything beyond that will have some crazy fee like 50 cents per mile or something like that. If you don't drive that much then it isn't a concern. The upside is you'll get a new car every couple years when you lease a new car, and during the lease time all repairs for non-consumable items (consumable items being tires, brakes, etc.) are covered by dealer at no charge to you; the downside is, as long as you're leasing, you're no closer to owning any car no matter how much money you've paid over time. The only way to apply the money you've paid into a lease to owning the car is if you opt to buy the car at the end of the lease. But none of the money in any of the leases before that car's lease will be used toward buying the car.
When you buy the car, unless you can plunk down all the cash to buy it, you'll have to finance it. When you finance it, the bank who holds the loan is the legal owner of the car until you pay it off 100%. At that point the car will be yours. If you want to feel like you own the car, that's the way to go because once it's paid off, you will own the car outright.
Here's my recommendation. Don't buy a brand new car. You'll be paying for all the depreciation. Don't lease a car because you'll never get any of that money back or be able to put it towards owning the car unless you decide to buy at the end of the lease, and there again you will have paid for all the depreciation. (I don't know if there would be a difference in the long run between a lease-to-own option like that, or outright buying from the start. You'd have to run the numbers.) What I recommend is that you buy a car that's a couple years old, which was a car that someone else leased and then returned at the end of the lease. You can find a car that has fairly low miles, you'll likely be able to pay little more than half the brand new price which will save you a ton of money, you can find a car in excellent condition because the previous lessee will have wanted to avoid paying anything extra for damage (I don't know if leases have any sort of a security deposit since I've never leased), and if you buy from a dealer who is an established dealer for the manufacturer (ie. a Ford dealer, a Chevy dealer, etc.), you can get the car as a "certified pre-owned" which means their service department will thoroughly inspect the car based on a checklist of manufacturer inspection points to certify that the car is in excellent condition. Additionally, you'll still have the car's bumper-to-bumper warranty that came with the car when it was brand new, and you can always extend that warranty a few years by adding a little bit extra to the monthly payment (the finance manager will walk you through your options regarding all that).
When I bought my current car, that's what I did. I bought one that was 2 years old for $15,400 (it was somewhere over $17K after all the taxes and fees, plus I chose to extend the bumper-to-bumper warranty) when the brand new price was about $35K, from the Chevy dealer who I talked into including the GM certification at no extra charge (normally that adds $500 to the cost, according to the sales manager), and it had only about 29,000 miles on it. The purchase also included 2 years of free inspections and oil changes. In my search for this model of car I found one that had only about 8,000 miles on it, but that added a few thousand more dollars to the price which I wasn't willing to pay, so I had to compromise and get something with more miles but a lower price. And since I was paying the loan rather than a lease I always felt like it was MY car, which I especially felt once I paid the thing off entirely so I own it 100%.
To be fair toward leasing, I do also have to add one more story. Some relatives of mine live way out in the country and the long road to their driveway used to be gravel, which was very rough and washboard most of the time. They leased all their vehicles for about 20 years because that road beat the hell out of everything they drove, and if they were to just buy their vehicles the repair costs would have been huge. Once their road got paved they began buying rather than leasing because their cars and trucks started lasting a lot longer. So in the case of their circumstances, leasing was the best option.