Id recommend a revolver for a first hand gun, and for home defense. Get an automatic for a second pistol. But that's just personal preference talking.
.40S&W is definitely more accurate than the .45ACP. We went through this here a month or two ago. .40 is a smaller round than the .45, with higher velocity. Simply physics tells us its more accurate. I like the .40, its small enough to accomodate approx the same amount of ammo in a clip as a 9mm, but similar knock-down power to a .357 mag. That is why cops use them.
I agree with the above statements however, that a 9mm is cheaper to shoot if its just for plinking. But if its also for home defense, Id look closer at the .40S&W. .45ACP's accuracy is fine for home defense, and has better knock-down power, but isn't as ideal for plinking due to accuracy. But a first-pistol owner would likely not notice the accuracy difference anyway. I think Ive demonstrated each round type has advantages and disadvantages, the .40 being the middle of the road, .45 being better for home defense, and 9mm being better for plinking. So choose which of those fits your needs/wants, and go buy it.
Id stay away from a Desert Eagle for a first gun. I love mine, in fact its my favorite pistol, but its not a good choice for a first-pistol purchase. They are, however, remarkably well designed and built. Awesome gun. Mine is a .44mag is feels smooth as silk when I shoot it. Double springs, amazingly easy to take apart and put back together, shoots magnum rounds otherwise limited to revolvers... the Israeli's really know how to make a gun.
I wont get into brand names because like car audio, much of it boils down to personal preference.