I've used Hagerty on and off for about 20 years now. I've greatly appreciated their service as well as their coverage. If you are putting less than 2500 miles/year on the Celica, I think their services are what you are looking for. I've seen it mentioned that Hagerty's premiums are a bit steep. I think that may be the case, but I've never had to argue with them over covering repairs or the value of my vehicles. They are more in-touch with the classic car enthusiast market than most automobile insurance companies are. They understand that most classic vehicle owners will do their own work, source their own parts, and most likely keep that classic regardless of the accident damage that occurs. I've used or looked into other insurance companies. I'm sure there are other good ones out there now, but I feel Hagerty has a better understanding of the classic enthusiast and the classic market as a whole.
Nationwide, Allstate, State Farm, and Farmers all have divisions that take care of classic car owners, but it's not their forté. Most will value the car for its tax value or somewhere in that ballpark, undervaluing the car. In most cases the only way to get them to agree to a larger declared value is to have the vehicle evaluated by an appraiser. Not to say their method isn't a good way of doing things, it's just more expensive than I'd like. Hagerty keeps up with the current trend of classic vehicle values. Hagerty will know your car's value pretty well and they are open to discussing any discrepancies. They even have vehicle valuation tools on their site to illustrate this. So, they'll understand that a 1969 COPO Camaro is worth more than $4K. Hagerty also publishes a magazine for their customers. The magazine dives into the trends in historic car values, in fact the 80 series Land Cruiser was highlighted in their most recent issue.
Hagerty offers several services to their customers, the handiest one for me has been flat bed towing. My Mustang sprung a pressurized oil leak at one point and I was forced to pull off the road. The thought of getting a regular tow truck to bring the Mustang home didn't sit well with me. Fortunately, as part of their customer support, Hagerty gives everyone the option of flat bed towing to their house or to a shop. I appreciated the fact that their towing service didn't do anything to my premiums, however the speeding ticket I got did.
Sales pitch over...
On the note of inspection, I can't really offer much info up on this. My car had been registered here back in the early 90s, so it was still fresh in the NCDOT database. I was told that their inspection isn't that big a deal though. They are mostly trying to verify that the car is what you say it is, nothing more than that.
Edit: Above I mentioned that insurers use the tax value of a vehicle, this is wrong. They use an agreed upon value.
Edit 2: Hagerty does keep up with current trends, but also uses valuation guides (Old cars report price guide), professional appraisers, and research conucted by an underwriter.