In my experience and the experience of many others I would stay away from the 05’s. Not that all 05’s were problematic but it’s more likely with the 4 speed trans being the weak link on those cars. 2008+ would be better for the LS3 but you’ll be hard pressed to find a nice one in your budget without tons of miles. These cars run for a long time so miles aren’t an issue. Figure out what options are a necessity. I’ve owned two vettes, my first was a 1LT and my most recent was a 3LT. After having the 3LT package I likely won’t buy another one without it. Go for the newest, lowest mile vette you can afford and good luck in your search