Best way to store user-uploaded files in a webapp

Your question is too broad to really be helpful; best approach will depend on your specific requirements. Nonetheless...

Programmers are constantly tempted to plonk files into the database. Resist. It just adds a layer of complexity to everything you try to do with them thereafter.

For my experience, whilst using a hashkey as the local filename was my preference, it didn't really work out because our files weren't restricted to images: the non-images need a filename to serve back to users, and the uploaders don't particularly like having their files radically renamed since it makes it impossible for them to know what file is what.

As for images there is some non-trivial work to do in rescaling to various sizes/thumbnails.

That is a big question.

Related to your picture use-case this is the domain of a picture-server which usually is a complete separate part of application. They handle lifecycle and resizing of images (one picture is stored/resized to different sizes). As far as I have seen such was never implemented by a BLOB column from SQL, but by straightforward normal file on disk.

Also have a look at a (infrastructure example from facebook)

Generally the product has to align to your concrete requirements (file-size, number-of files, load). In most cases you really don't want to build all that stuff from scratch... Though if your requirements are lower end (just a few users uploading files rarely) you could just save these files on disk and save the path as reference in your other data (e.g. column in RDBMS).