your question is too broad for a really focused answer...
308 vs 223: i have both, and certainly like the 308 better. however, being new to rifles, you will probably shoot better and more often w/ a 223... we are talking target shooting, and not hunting, right?
special considerations for aiming: none, really. especially at the shorter ranges (250 yards and in). the scope handles that for you. at longer ranges there is definitely a science to the process, but as a new shooter, most of your shooting will be done at relatively close range. even the 223 produces enough velocity that once you get your scope sighted for 100 yards, you will at least be on paper for 250 yards and beyond. you will certainly have to compensate for bullet drop, but the trajectory isn't like falling off a table.
there are a lot of choices in rifles, too. available from the factory are rifles that weigh in at around 5.5 pounds (remington ti, weatherby ultra-light) to big-barrelled beasties that will come in at 10 pounds and more (remington vls, ruger target, etc).
generally speaking, it is easier to get a heavy barrelled rifle to shoot well (tight groups), but they make poor hunting rifles due to their size and weight. conversely, the ultra-lights make excellent hunting rifles, but make very poor target guns because they kick so damned hard, and the short, thin barrels don't get as much velocity and are harder to shoot accurately. then there are the sporters, which are the most common.
if you can clearly define how you want to use your rifle, it becomes easier to choose one, and what accessories you want (if rifle shopping doesn't give you a headache, i promise, scope shopping will).
if you go w/ a bigger gun than a 223 (knowing what i know now, if i was looking for a first rifle that was to be mostly a target gun, i'd give a very long, hard look at rifles chambered to 243), and after shooting for awhile recoil becomes problematic, don't distress - that can be helped.
good luck.
