"Adrian" wrote ...
Your advice would be appreciated: I plan to commence
recording some meetings.

Are these meetings using some sort of sound reinforcement
(PA) system already? i.e. can you tap into an existing setup,
or do you have to roll your own?

The meetings will consist of singing accompanied by piano
followed by a talk.

Is the piano player doing the singing?
Is the lecturer doing the singing (or in the same place)?
Or do you need separate mics for:
piano, singer, and lecturer?

The recording device will be a Del Latitude fed
from a Behringer 1204 thru a UCA202.

There appears to be more than one mixer called
"1204" One of them has built-in USB. Exactly
which one are you asking about?

Thus far every microphone

What microphone(s) would that be?

I have plugged into the Behringer

Assuming you mean the 1204 and not the UCA202?

gives, insufficient signal.

How are you measuring "insufficient signal"?
In the recorded computer file?
At the computer recording application input?
At the mixer LED level meter?

With the faders at max I seem to barely have
enough sound.

What does "enough sound" mean?
Are you using mics that require phantom power?
Is the phantom power turned on?
Do you have the microphones plugged into the XLR inputs?
Where do you have the gain knobs set?
Does the mixer, etc. produce "enough sound" with
any other input?

At this point I am thinking of three mic.'s I could go
to four if that would be better.

What would the fourth mic be used for?
Typically, fewer mics are better. For any
number of reasons.