I'm delighted that the Internet speed problem
has resolved itself. I'll confess to being a little curious as to the
cause, but it's not worth investigating a solved problem.

Some larger applications may require more RAM, as Ian suggested. But
you should be OK for a while.

Let me suggest that you install a firewall. You should do this before
anything else, even before downloading the security updates. It's
easy to do, and will give you a bit of experience with the Ubuntu
software installation process.

I recommend "Firestarter". It's small, easy to install, and trouble-free.

Step 1: Make sure you have the right software sources enabled:

-> Select "System" | "Administration" | "Software Sources". You will
be asked for your password.

-> On the "Ubuntu Software" tab, make sure that these lines are checked:

* Canonical-supported Open Source software (main)
* Community-maintained Open Source software (universe)

and, optionally:

* Software restricted by copyright or legal issues (multiverse)

You should probably leave "Download From" as "Main Server". Click
"close".

Step 2: Find, download, and install "Firestarter":

-> Select "System" | "Administration" | "Synaptic Package Manager".
You may be asked for your password.

-> Click "Reload".

-> Click "Search". Enter "firestarter" (no quotes) in the search box,
and click "Search". It should find only one package; click on the
line and read the description.

-> Right-click on the package line, and select "Mark for Installation".

-> Click on "Apply" (in the top menu). It should download and start
the installation automatically. The default options should be the
right ones: just make sure that the detected "network device" is your
dial-out (ppp0) device.

Later, when you're installing all those updates, you'll be protected.