Acceleration can be very important if the semi that hasn’t noticed the red light is barreling down on you. There have been a number of times when accelerating quickly has prevented me from getting in an accident.
Now, regarding 4 vs 6. It would be really good if someone shot the automotive marketers who make such a big deal out of the number of cylinders. My 4 cylinder Toyota MR2 is significantly faster than a Duesenburg Model J, which had 8. In more modern comparisons, the 4 cylinder Honda S2000 will outrun an 8 cylinder Crown Victoria.
In short, number of cylinders is absolutely no indication of how fast a car is. What you want to look for when you want to know how fast a car accelerates is the 0-60 time. “Fast” these days is generally considered to be anything below 5 seconds. (For the record, I think this is insane - 5-7 seconds is plenty fast enough for normal street driving. 5 second 0-60 times used to be the realm of Lamborghinis and Ferraris. Your 4 door family car does not need to move that fast, ever).
In the same vein, the number of cylinders does not indicate fuel efficiency. The 4-cylinder Ford Escape I drive at work gets almost the same mileage as my 6-cylinder Acura TL. And the TL is faster and doesn’t break all the time, unlike the Ford.
In short, you need to look at the individual numbers for the cars you’re looking at rather than worrying about how many cylinders it has.
As to safety, most modern cars are going to be very safe. Even the ones that get a mid-range safety rating are exponentially safer than the cars you rode around in when you were a kid. Wrecks which would have killed you 20 years ago are now survivable to the point that you can walk away from them.
If a car doesn’t meet (high) minimum safety standards, it’s forbidden from being sold in this country. So my recommendation would be to find a car you like, and buy it.
15 grand can easily get you a quick car. You could probably get that Acura TL I mentioned for around that. Look for a 2006-2008 model year - they’re very nice cars, have fantastic features, are roomy, and from personal experience I can say that they’re quite a bit faster than the official numbers claim in acceleration while still getting 29-32mpg highway.