Yes Tony a variety of different types of car insurance are available.
Fully Comprehensive are sometimes referred to as 1st. Class & costs 15K up
There is also 2nd. class available which I believe is about the equivalent of 3rd. Party (not sure if Fire & Theft are included) I believe it is about 5K.
Up until a few years ago the Government used to insist that all drivers had to display a windscreen sticker showing a very basic level of insurance (I believe the equivalent of 'Road Traffic Act' insurance in the UK) which cost about 1K - If you purchased comprehensive insurance many companies would 'throw this in' with the comprehensive cover.
Personally i would not entertain buying anything except fully comprehensive. It is not only the traffic conditions (although that plays a large part

) but also the uncertainty of what is, or is not, covered that would concern me.
I have just paid the annual registration on my Honda City & it was just under 2,000 baht (1,9 something ). From memory it was between 4K & 5K for a large pick up.