After reading the guide I believe it may be overheating.

The digital thermostat will go blank after running for 10 min or so and the display will turn back on in about 20min. The system is not able to keep the house over 60F. I don't think it has been cleaned in the 4 years I've lived there and not sure about before that.

How hard is it to simply clean the unit? And is there a good guide for doing this?

I want to be safe while trying this so is the only thing I need to do is throw the circuit breaker for the furnace?

What about the gas that is running(I guess it would just be the pilot that is lit) but do I need to turn off the gas to it, or is it safe with just the pilot running?

The problem could be many different things. I do not suggest you try and clean the unit. But I do suggest you call for Professional On site service to get it fixed properly.

If the thermostat is battery operated or has battery's in it you might replace them since they probably have not been changed in 4 years. Also make sure the air filter is clean or replaced.

I'll have a look for a battery and make sure filter is OK.

Is there anything that I should look for when looking for someone to come fix it? (I'm not sure what type of company to even look for this, I done a yellow page search for HVAC and not sure even what I'm looking for however)

Also roughly how much does inspecting / cleaning cost? The unit is actually underneath the house and is kind of tight but enough room to sit and work on the unit.

Cost for service is different all arounf the country.

Look under heating companys in the yellow pages