Hey John, 

A few questions first.

Is the chimney functional?  Is the flu venting anything in the home (i.e. furnace)?  Does the chimney go through the roof, or next to the roof on the eave or rake?

If the chimney is not functional and it does not vent anything in the home, you may want to address the problem at the roof by closing it off.  This will make sure no bugs or water can enter into the home.  If the chimney is through the roof, you will need to tear the structure down below the sheathing, install blocking around the chimney box, and install new sheathing over top the chimney.  Exterminators are always the best experts to call for bug problems.  If they keep coming back, it may be time to try a different company. Hope this helps!

Eric Consuegra

AROCON Roofing and Construction, LLC

On the squirrel removal, best to call a trapper or get a trap. 

That area agains the home can be covered with some heavy guage counter flashing and sealed up prior to that with some fast setting mortar. 

here is a link to a good article on How to get squirrels out of an attic.

http://www.aaanimalcontrol.com/professional-trapper/squirrels-attic.htm

You can proform both jobs at the same time if you are good at what you do. I have in the past grinded a Grove in the brick chimney all four sides then used a brake to bend a little half inch lip on the top of my flashing metal flashing into massonary Grove then caulked you will never ever have to worry about again in your lifetime Only reason I did massonary work first is because I didn't want to get my shingles all dusted.

Tear off cimney from roof, cover plywood hole, and install roofing to match

Masonry work first. Best, Ken

The masonry work should be performed prior to repairs to the existing roofing, unless the roof is leaking, whereupon you may need to make intermediate repairs to stop the leaking while the masonry work is performed.

Each case is unique but in general, the chimney should be done first. Special attention should be paid to the roof flashings around the chimney.  If the flashings are behind the stone then make sure they extend far enough into the shingles so the new roof can be flashed properly. If the flashings are surface mounted and there is a counter flashing then the roofer should have no problem making the chimney base watertight   

It is always better to repair the chimney prior to any roofing work. This way the new roof doesn't get damaged. 

Our recommendation would be to do the massonry work first and then roofing for a few different reasons.

1.This gives the masons freedom to step and walk on the roof without causing damage to the new shingles. 

2. You will want to make sure the new flashing that is intstalled around the chimney is installed correctly, accounting for any masonry changes and is not damaged due to installation.

3. Ultimately, that the new roof is not damaged and that the warranty does not get voided. 

Definitely before you do the roof, masonary work and any flashing around the chimney should be done prior to starting on the roofing.

An enclosed Chimney Cap if they're coming throught the top of the Chimney.

What did you decide to do then? Following the proper process would help.

You're not looking for a brick mason.....your looking for a landscaper expirenced in hardscapes.....brick masons typicall only deal with installing brick facades.....pavers require grading,fill material (compacted correctly), and then paver install....not something a mason would have knowledge of...