I suggest downloading the trial version of FMP and playing with it and the free tutorials to see if you can make it work for you. A lot depends on your own expertise and how much time you want to spend learing how to do this.
Two key points drawn from your post:
You can easily import excel spreadsheet data into filemaker. If the first row consists of unique column headings, filemaker can even make these the field names of a new table in the database. (Try it with the trial install).
You can use a feature called Instant Web Publishing (IWP) to publish a simple database to the web. There are also hosting companies that will host a database for you.