Are you a:
Cookie?
My beginning (sort of) describes the way I'm created,
Cook (well, bake)
The importance of my ending can't be understated.
Without the "ie" ending you'd be left with a "cook," which is quite a different thing...
Before I am finished, I'm nothing but money,
Before it's a cookie, it's dough (and dough is a slang term for money).
Though throughout the whole process, I'm sweeter than honey.
Cookies are deliciously sweet - as dough or as the finished product!
I'm used by a spider that looks for his house,
Perhaps this one is a bit of a stretch, but: web spiders (also known as web crawlers) sometimes use cookies (the internet kind!)
And strange things can happen when I'm received by a mouse.
Referring, I assume, to the children's book If You Give a Mouse a Cookie.
Be branded a monster if you love me too dear,
But not a monster that many have reason to fear.
Cookie Monster - a monster indeed, but not a scary one!
And the title:
I assume refers to a chocolate chip cookie!