Most of these comics have pretty decent art, as that is important to me. Some, like XKCD, don't even try to be particularly artistic, but make up for it in other ways.
These can be read in any order, as none of the comics really have any relation to each other. They may occasionally have short story arcs, but generally not more than 4-5 strips long. They may also have recurring characters, but no real character development. There is no need to read the archives to get what is going on.
These generally have short to medium story arcs, but the characters involved can change over time. Reading the archives isn't generally necessary, but can give useful context.
These have long-running stories (or may even be one long story), and should be read from start to finish.
These haven't updated in quite a while.