It's quite possible and the fact that you want to publish this to the web shouldn't be much of a factor.
I suggest that you have submitters create and enter new records in the same table as you have for your reviewed/approved data, but use a status field to indicate whether or not the record has been approved. You can use finds, relationships and portal filters to control whether you are looking at "unapproved" or "approved" records. You can then use manage | security to set up accounts with privilege sets that control which records can be viewed and which can be edited based on both the privilege set specified for that account and the value in this status field.
See "Editing record access privileges" in FileMaker Help and check out this particular sub section: "Entering a formula for limiting access on a record-by-record basis" for a detailed description of how to set this up.
Thank you for the tip on where to look in the help section, it is telling me pretty much everything I need to know. Now I am just confused about the part where you said that I can use finds, relationships, and portal filters to control whether I am looking at approved or unapproved records. I am not sure what you mean by this or how to go about doing this so some clarification would be great. Thank you.
There are lots of different ways to use these basic database techniques to work only with approved or only with unapproved records on a layout.
This script would pull up only "unapproved" records so that they can be reviewed and approved:
Enter Find Mode //clear the pause check box
Set Field [YourTable::ApprovalStatusField ; "Unapproved"]
Set Error capture [on]
Perform Find 
Do this every time you access a specific layout and you'll only see unapproved records on this layout.
On the other hand, if you include the "approvalStatusfield" in your sort order, your records would be grouped by approval status and this makes it possible to collect counts and other subtotals from data in each group of records if you also use summary fields and a sub summary layout part.
Portals can include a portal filter to only display "approved" or "unapproved" records. Set up the expression like this:
PortalTable::ApprovalStatus = Globals::SelectedApprovalStatus
and you can set the Globals::SelectedApprovalStatus field with radio buttons or a pop up menu and the same portal can display either approved or unapproved records based on the value selected in this field.
More options are possible.