Well, I had never tried that but Microsoft says:

Planning a Microsoft(r) SharePoint(tm) Portal Server Deployment White Paper:

SharePoint Portal Server and SharePoint Team Services

If SharePoint Team Services is installed on the computer on which you want
to install SharePoint Portal Server, you must uninstall SharePoint Team
Services before installing SharePoint Portal Server. In addition, you must
delete the following registry key:

HKEY_LOCAL_MACHINE\Software\Microsoft\Office\9.0\Web Server

If you install SharePoint Team Services after installing SharePoint Portal
Server, you lose the following functionality from SharePoint Portal Server:

* Discussion items are not included in the index and are not
available for search.

* You do not receive notifications for subscriptions to documents or
folders in the workspace when you subscribe by using the Office
collaboration toolbar. The Office collaboration toolbar is available from
both Office and Internet Explorer.

* Subscriptions made by using the Office collaboration toolbar and
all discussions are stored in SharePoint Team Services. These subscriptions
and discussions are not backed up during the SharePoint Portal Server backup
process.

So, I can build an MSDE database and my SPPS will talk to it?

According to
support.microsoft.com/default.aspx it is
not supported to run SPS and SPTS on the same machine.

Ok that's what I thought. As it was explained to me, team  services was
designed for less than 75 users and Portal for over 75.

Now my question becomes for Team services, which is better, the MSDE or full
blown SQL?

According to a Microsoft white paper I have here
entitled "Installing Microsoft SharePoint Portal Server 2001":

----Begin Quote----
SharePoint Portal Server and SharePoint Team Services
If SharePoint Team Services is installed on the computer on which
you want to install SharePoint Portal Server, you must uninstall
SharePoint Team Services before installing SharePoint Portal Server.
In addition, you must delete the following registry key:

HKEY_LOCAL_MACHINE\Software\Microsoft\Office\9.0\Web Server

If you install SharePoint Team Services after installing SharePoint
Portal Server, you lose the following functionality from SharePoint
Portal Server:
• Discussion items are not included in the index and are not
available for search.
• You do not receive notifications for subscriptions to documents
or
folders in the workspace when you subscribe by using the Office
collaboration toolbar. The Office collaboration toolbar is available
from both Office and Microsoft Internet Explorer.
• Subscriptions made by using the Office collaboration toolbar
and
all discussions are stored in SharePoint Team Services. These
subscriptions and discussions are not backed up during the
SharePoint Portal Server backup process.
----End Quote----

You can find it at:
www.microsoft.com/.../installing.as
p
(watch for line wrapping)
It has a very well documented section about coexistance with other
products.

We run portal  and Team services  on the same server  (dual pentium 1
Ghz) - Portal was installed first and Team Services second - the only
problem we have ever had was a hardware failure. We have one portal
virtual server and 60 Team services sites that service 2600 users.

I think it depends on what you want to do with it, what machine you
have, how much users are supposed to hit that machine and what volume of
data transfer is expected.

Out of the blue I'd say full SQL server, but somebody else on this forum
might prove me wrong...

MSDE could work for less than 20 concurrent users, for more you will get a
lot better performance with SQL Server. By the way although Microsoft said
in the past that Team Services was for less than 75 users in reality it will
scale up to 1000 users easily depending on the box you have.

What is important to note is that SPS and STS are different and
complimentary products although they share a common name. (Ask Microsoft why
they are confusing everyone).

I can confirm that there is no limit on the number of users within STS.
Apparently the message that MS are trying to give is that if you have more
than 75 users you are likely to want to use the additional features within
SPS.