Demon of the Well
I play mainly alone and mainly for leisure, and in ports with the requisite functionality, my preferred settings are freelook on/default autoaim/no crosshair. In fact, I normally have the screensize maximized to the point where no status bar shows either, but of course I snap it down a peg every now and then if I need to check my health or ammo.
The reason for these choices is that I've been playing Doom since before the advent of mouselook-enabled sourceports, and so I'm so used to the quirks of the original autoaim behavior (e.g. having to make sure you don't throw a rocket into your feet if you're standing on a high ledge and a cacodemon is floating up towards you from a certain angle) that I simply feel more at home with it on. Freelook, of course, makes a relevant impact on this, in that it naturally invites one to aim vertically as well as horizontally, but I generally find myself aiming precisely on the horizontal axis and rather roughly on the vertical one, letting autoaim handle the finer points there....in other words, similar to how it helped in the original game (and it is an indispensable help in some situations, undeniably). Why do I use freelook at all? Well, it's actually mainly because I like to look at the scenery. As a matter of some kind of ersatz personal honor code, I try to refrain from doing things like chaingun-pecking snipers who are miles away (e.g. well outside the purview of autoaim) to death, or exploiting it in situations like the Plutonia example described by Feniks, unless it's the sort of map/mapset where doing that kind of thing is explicitly part of the intended experience. The lack of crosshairs is also an aesthetic thing, though I'm not above temporarily turning it on (or indeed, autoaim off) in ZDooM maps were you're supposed to hit tiny buttons across huge chasms or whatnot.
Do freelook/autoaim configurations drastically alter the difficulty level of the game? In some specific situations they can, certainly, to the point where I'd be disinclined to agree that either one renders the other obsolete; e.g. autoaim is indispensable in some situations in Doom, Boom, whatnot; and direct aim is very useful (or even mandatory) in specialized ZDoom situations, although one could probably learn to make due with either setting to a more or less adequate degree in the majority of situations, with enough practice. Incidentally, I can drop freelook and be back in the swing of playing well without it in the course of a map or so, but keeping freelook and disabling autoaim takes me a little longer to get acclimated to, as least as far as ordinary combat goes. What I have a harder time adjusting to these days, though, is playing with infinite-tallness enabled (which I still do sometimes just to remember how it feels).