Considering story tags I think most important is to describe its mood and unfortunately this is information newer available
Probably most important tad would be if it is consensual or not.
and something that briefly list story content
It is not that much important it it is furry or not, you will imagine characters in away you like yourself anyway

another thing I find irritating, is very long character names: something like "Sailor moon" gets pretty irritating after you read it 90th time
they should be shorter or replaced with nicknames

I am also thinking how to format dialogue properly expecialy if there are lots of characters talking

A- I think I need a hug.
B- No worries. I've heard the oven has a nice, warm embrace.
C- You idiots!

But that type of labeling also interferes with reading experience because you so read those labels
so using unreadable symbols may be better idea

#- I think I need a hug.
@- No worries. I've heard the oven has a nice, warm embrace.
$- You idiots!

Or maybe this way is even better
- I think I need a hug.
-- No worries. I've heard the oven has a nice, warm embrace.
--- You idiots!

if there are only 2 characters
Speech of one of the characters should always begin with blank like
and paragraphs could be separated with two blank lines

I disagree about use of quotes, because quotes are typically reserved for quoting or saying what you do not think (typically to express sarcasm)

valid use of quotes in dialogue would be if you write something like :
I heard Jenny saying "you are a loser" said Sally
Or
We all think you are "great cook" but please don't burn it next time
direct dialogue is not quoting unless story is written in a way where narrator is telling the story instead of story is happening by itself and thus narrator is quoting story characters.