We've leased several vehicles and owned several. It really depends on what you're looking to do. I know there is the comment about Dave Ramsey and his philosophies, but that's very general to the public as a whole.
Generally speaking, leasing is a better option for people who like to have new cars more frequently. The cost/month is generally lower, and the terms can be more flexible. The bad side is that any equity you have in your current vehicle is lost unless you plan to lease to own.
All of your equity will go into a new vehicle if you choose to purchase it, but your payment/month will likely be higher. It just depends on which you're comfortable with.
When I was laid off last year, I chose to purchase my company car. We held onto it until March and used it as equity (along with another vehicle on a new car). We didn't need a new car, but we didn't need the 3rd car either. So, we were able to save $200/month in payments with the new arrangement. Because I'm not as financially savvy as some people, I ran it by our corporate controller who said it was a great deal.
There's nothing wrong with dealer financing as long as your credit score is good. We're fortunate to have high credit scores and to qualify for most financing options. We could have either taken 0.9% financing or $1500 cash incentive. I'd never have guess the incentive to be better, but the numbers showed we saved ~$8/month with the incentive.
I'd always recommend sites such as NADA (national automobile dealer's association), Kelly Blue Book, Edmunds, Car & Driver to verify the pricing (for both your trade and the new vehicle) as well as ratings and opinions. We've walked away from several vehicles because the resale value wasn't good or because the opinions were less than favorable.
Good luck. It's not a pleasant experience, but cars are a necessary evil. With gas prices climbing again, I'd recommend taking that into consideration. I'd much rather have the 22 mpg in my old Taurus vs. the 16 mpg in my Pilot currently.