The main practical disadvantage of single-actions is that they take longer to operate because they must be manually cocked and spent cases must be ejected one-at-a-time. Therefore, they are not suitable for timed shooting competition and they aren't the best choice for self-defense. Even though they are slow to operate, you can hunt, plink and get quality marksmanship practice from a single-action.
Do single-actions have any practical advantages over a double-action? I can't think of any (and I own and shoot single-actions quite a bit), except that you can get a high quality single-action for less $$$ than a comparable double-action, even though the difference isn't much when you consider how much ammo costs. You could argue that a single-action is stronger and less likely to develop problems than a double-action, but double-action breakdowns are uncommon enough that this isn't a real practical advantage to me.
If self-defense is on your list, get a double-action and fixed sights are OK. If you want to hunt, get either SA or DA as long as it has adjustable sights and a reasonably long barrel (hunting regs may specify 6" minimum) - the ability to mount a scope might be important. If you just want to plink, get whichever looks best. If you want to work on your marksmanship, get either one, as long as it has target sights (a DA is easier to shoot well if it has a good trigger, but learning to shoot a SA well will make your DA shooting even better).