Car insurance...

Ok, I just moved and, after giving my current (supposedly cheap) insurance company my new address, my car insurance went up - again...  So, I made the mistake of going to a "comparison" website to see what's out there and now I'm getting bombed with phone calls, emails, text messages and even letters.  
 
Now I've got a perfect driving record, a car that stays parked in a garage most of the time (less than 5,000 miles driven per year - I use a company truck for the longer drives) and the car isn't worth much.  I don't think should have to pay a lot for it.  I also found that I'm not even covered if I run into a deer or if someone steals things out of my car!  So I'm creating one of my usual spreadsheets to determine what I REALLY need before talking to each company.
 
I've done some research already and part of today has been set aside to get this figured out the rest of the way.  That said, does anyone have any tips, tricks and pointers they'd like to share?  Any do's or do not's, or pros and cons about companies?
 
Last time, I had to go with who I did (Progressive) because I had had a lapse in coverage when my previous car died (for several months I was only driving a company truck belonging to a friend's business and he had the coverage).  Now that I've had coverage for over two years I won't have to deal with that part.
 
I hate insurance!  It's always a lose-lose situation.
 
Note that I'm not a veteran so companies like USAA are out of the picture.
 
Thanks!

'Tis what I'm learning.  I've had more near misses with deer up here than with cars (actually not even close in comparison) so that's why I'm curious about that one.
 
Obviously, not having a lot of money causes all sorts of weird issues that most people don't have to worry about.  I've got a '96 Toyota Camry that's probably not even worth $2,000.  However, it's ALL I have so I'd be royally screwed if something happened to it.  A bit of a catch-22.  Plus I don't own the home I'm in, so I may look at combining renter's insurance to get a discount on the car insurance.  Did I mention I hate insurance?  Yeah...
 
It's very tempting to take the lowest, legal insurance I can find from some unknown, online company, but I may come out better spending an extra $10 or $20 per month to get what I need from a more solid company.
 
I'm creating a grid in a spreadsheet so I can call each company to find out exactly what their premiums are for each.  I can think of a LOT of other things I'd rather be doing with my "day off," but it needs to be done!
 
Thanks for the reply.

The big cost, and therefore the big price in auto insurance is liability. Think about it. You crash into a parked Yugo. Your car is totaled if it will cost more than two grand to fix it. You get a check under collision for the blue book value of your car. The Yugo owner sues for $19.99, and the jury only awards $4.50, and he gets a check if you have that much coverage unser liability. If you crash into a Ferrari then you might need $200,000 coverage before the owner goes after your house, if you have one. If you hit a child rendering him a vegetable requiring twenty years of coma center care at $300,000 a year, someone is going to have a very very big bill. Liability insurance does not protect you above the assets you have, or are ever likely to get. If damages are astronomical and you are poor, then you are, in the terms of the profession, "judgment proof." A six million dollar award against a pauper is just uncollectable. You can generally get coverage for liability above about $500,000 only by buying an umbrella policy, and even those are often limited to a million or so. But if you have no assets, and do not expect ever to have a lot, and you do not mind having your future wages garnished for the maximum allowable (typically 25% of your after tax income)  forever, then a low liability coverage may be enough for you, if not for your victim.

Everyone probably has their own opinion on what is a fair price to pay for car insurance. But my wife and I cut our cost almost in-half a few years back by switching from a very major US auto insurer to Geico. And after a few years (due to some other reason not affiliated with the auto insurance) then switched to Farmers where I feel we also receive a fair price. Cost is also cut by also including home insurance along with the auto. I guess my advice would be to shop around a bit.

In the UK we just go to the one with the Meerkats and get a free toy.

Ok, but what do you pick if you don't have a job?