Generally, a sound person would prefer you to have your guitar up on full volume for sound checks. This means that they can setup the channel for the highest volume. The pedal is a different matter, because you dont want to cause clipping at the output of the pedal or even the input of the DI (if it has no pad on it).
I would suggest you get an amp and use it for you onstage sound and then place a mic in front of the amp (eg. a shure SM57) and then what you hear onstage is pretty much identical to the sound out through the speakers. I have found in the past that DI's on electric guitars sound very harsh, especially with distortion and other effects. By using an amplifier with a mic you get a much nicer sound and the sound the audience hears is what you want them to hear. You would no longer need guitar in a monitor either.
As said above, sound checks are used to set levels (both front of house and monitors) and also to make sure that everyone (including the sound tech
) is happy with the sound. However, if you use the same amp for practise and gigging, the setup should be about right each time. You dont really need a huge amp, its only going to be used for stage sound, so a smaller, nice sounding amp is ideal.