The style of rakes on houses is indeed a regional thing. Here in MA, it's very common for the rake trim on a roof to be applied with no overhangs. The trim is spaced off the sidewall sheathing with a piece of 1x3 to allow the siding to run up under the rake trim. When the roof is shingled, typically, there is what we call a "kicker course" of shingle, laid end to end up the rake. This shingle overhangs the rake trim by about 1/4 inch. When the courses of shingle are laid on top of the kicker course, the roofer can reach under the course and run his knife along the kicker course in order to trim the shingles to a nice even edge. The kicker course also serves as a backer for the shingles that overhang the edge, making them less susceptable to sagging or breakage. You need to limit the overhang to about 1/4 to 3/8 otherwise you're setting yourself up for a problem, as a larger overhang will lead to failure.
Sometimes if a customer requests it, we will apply a drip edge to the rakes. It's a matter of preference, the above-mentioned approach is tried and true. If you're in a situation where you would be roofing over an existing roof, applying a drip edge serves to cover the existing kicker course and roof so that you don't get the appearance of 5/8 of an inch of roofing material showing at the edge of the rake trim.
In the case of the vinyl siding... the right way, oh wait, there is no right way to install vinyl siding! Typically in an effort to keep the water on the outside of a vinyl job, the side J channels are capped by the top J but the top J is cut a and the "bottom" of the J is bent down on both ends so that it interlocks (more or less) into the side J channels. This causes water in the top channel to drain down along the side J channels. No caulking is used. If you have read any of my previous posts, you know how I feel about caulking and how it can really screw up your project. Besides, caulking vinyl is an excercise in futility as the product movement due to temperature swings far exceeds the elastic capabilities of any caulk.