PostgreSQL has phpPgAdmin: http://phppgadmin.sourceforge.net/doku.php?id=start
It also has a native Gui client: http://www.pgadmin.org/
PostgreSQL is the single most reliable piece of software I have ever used. I have used it as the back-end for my projects for over ten years. I have pounded it pretty hard, and have yet to be disappointed.
Edit: I have put it in situations where you would THINK data should get messed up, yet it never did. I have filled up drives, lost power, screwed up mount points etc. etc., and have never had anything -- ANYTHING -- get corrupted. This is in stark contrast to the other databases I have used.
MySQL may have MySQL Workbench, but PostgreSQL has PGAdmin which provides a really nice interface too.
Screenshot of its kick-ass graphical EXPLAIN panel.
I usually write my table and index definition SQL in it because I can't be arsed to type it out every time.
http://www.pgadmin.org/ is really nice.
(I like it better than MySQL workbench but that is just familiarity and personal preference.)
There is also this
http://www.teampostgresql.com/
which is like phpMyAdmin for PostgreSQL.
PostgreSQL has CTEs and window functions. MySQL doesn't (as far as I know... someone correct me if I'm wrong).
Both of these are pretty huge when it comes to writing complex queries.
PostgreSQL has http://www.pgadmin.org/ . It is a pretty awesome for administration
It's just standard defense-in-depth.
First, for simple websites usually you'll run the database and web server on the same physical server. So there's no need to have your database listen to incoming network connections or to open up the database's port on your firewall to listen for incoming connections.
For more complex websites where the database and webserver run on separate servers, really the database only needs to talk to a very small subset of IP addresses -- e.g., the web server, maybe a few computers that have applications that need connect to the DB directly (e.g., to directly update information in to the database), and maybe the computers of some local developers who are actively developing the website (so they can use tools like pgadmin from their local computer).
From my viewpoint its hard to imagine scenarios where your actively used database should be directly accessible to the entire internet (with all the users logging in straight to the database user with DB username/password; and then running SQL SELECT/UPDATE statements directly on the server). Most users will be clueless as to use database clients to login to a database and will not know how to write SELECT/UPDATE commands to use it. It's a bad idea to give random users direct access to your database, unless you've really field tested it; as even if you've appropriately limited access there's still the potential for things like denial of service attacks (construct complicated queries with regex that take forever to compute).
There are graphical tools for pg database administration. 10 years ago i used this one but maybe now there is something better, I dunno. It can create tables, indices, etc.
Don't forget that you can also use execution plans. If you use pgAdmin you can also get a graphical overview. I think it gives a good view on where optimizations are needed.
The links are for Postgres, but I think MySQL should have this ability too.
Dreamweaver isn't really used by web devs as far as I know. By that, I mean I've never seen a professional use it and I've heard only bad about it. I have not used it myself, so can't say how suitable it might be for whatever you're trying to do.
This is something you'd usually write by hand, assuming that you wanted a public facing website. It would require some knowledge of basic SQL and any server side language. There's also a number of types of DBMSes (which is what Access is), although for such a basic use, it wouldn't matter too much. I recommend Postgres if you have no other idea about what to use. Postgres also has a pretty simple full text search capability built in, if your search functionality would need that (it would if you want to search for things like articles or reddit posts).
And then you can use any plain text editor you want. Sublime Text, Notepad++, Brackets, and Atom are some examples. Or vim if you're a masochist.
But if you just want an admin interface to visually see the database, then there's a number of tools for this, all DBMS specific. For example, Postgres has pgAdmin. That's a desktop program, not a web front end. There's probably several web front ends available, but I don't know any well enough to make recommendations.
Looks like they have Windows and OSX builds. Sadly, no Linux pre-compiled builds, though Ubuntu appears to have it in their repos.
Here is the list. I have no idea which is closest to SQL Server Management Studio. pgAdminIII looks pretty close.