> OP-AMP does. Is it a good option for me?

Possibly, if the 1V signal is "weak", ie is high impedance
and cannot drive much of a load. An op amp will be able
to amplify such a weak source

> Or can I use a simple transistor like the BC547?

Yes

> I only have a +5v supply. The signal is about 4 kHz.

> I bought a LM741, only to find that it needs 18volt Vcc. Right?

A 741 won't be any good at 5V. It's supply voltage range,
depending on type, is +/- 3 to +/- 22

> What should I get and what should I look for when selecting
> the OP-Amp

One that can run on a single-end power supply, eg +5 and 0,
there are many around. In your application either the op amp
should be wired as a comparator (ie it will have very high or
open loop gain) or use an actual comparator, eg LP311

Although using the PIC's comparator is a good idea, if you're
thinking of using this with other micros, then you may not always
have comparators or ADC available, so it would be better to
use external amplification to make it universally portable

> If you know of a good OP-AMP HowTo on the net, a link would
> be fantastic. (I have only googled a little so far.)

Googling for "op amp tutorial" gets a few results

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