Most reliable??? Revolvers, Glock, Springfield XD, M&P, FNP. These seem to be the favorites anyways. Revolvers are reliable by nature, the others are striker fired pistols with proven backgrounds, at least on the internet forums, I'm assuming that since you put this under autoloaders that the revolver is out. I love my XD and glocks have been a proven model for a long time.
Certain calibers also tend to have less bugs. .25 and .32 autos as well as anything rimfire can be picky about ammo and reliability for rimfire is always a matter of question. 380s are a bit better but are still is a group of firearms that can be finiky. Anything else will give you a wider selection of more reliable guns.
On 1911s, best reliability from the thousands of posts that I've probably read on the matter claim that full size .45ACP (in other words a standard 1911) that are mil-spec tend to be the most reliable, at least without spending thousands of dollars.
My little motto is the tighter the tolerances, the more accurate the gun, and the less reliable as well.
And yes, this question has been asked a billion times from bar rooms to online forums and a lot of the answers come down to a matter of opinion.
I think to answer your general question (If I'm reading it right) there are plenty of guns around for under 1000 dollars that are very reliable. Glocks can go for less than 600, SAs are around 600-700, and reliable 1911s start at around 700. I recommend that you find some guns in your price range that "fit" you and then search the forum to get peoples opinions about how accurate they are.
,the gecko