Car insurance

I was looking at the price comparison websites for car insurance, and found one that was really cheap, then I typed in their name Mymotorquote on google, and found a review site filled with negative reviews. While there, I had a look at the other reviews, and it seemed like most of them had negative reviews. It was quite alarming to read that peoples insurance policies were being canceled, and the prices being changed randomly. Are there any sources that list information on decent and reputable companies? I have a full UK automatic only licence, but was told I could drive manual on it for 1 year after I originally moved to Britain. I haven't been here for one year yet and still have several months left to practice on it. I'd also like to ask, for insurance purposes, does it matter if I have been driving for 10 years in the USA? Or is it, as far as theyre concerned, I am a new driver since I just got my British licence this year? I'd like to think that I am a better driver than an 18 yr old who just got his licence, but I also know that they calculate quotes with computers and they don't really seem to differentiate between someone who has driven for a long time overseas, vs someone who has just got their licence in the UK with 0 driving experience.

Never heard of Mymotorquote so I can't comment on that, but addressing some of your other queries:

I have a full UK automatic only licence, but was told I could drive manual on it for 1 year after I originally moved to Britain.

You would actually be driving a car with manual transmission under your U.S. license for that year.  After the year is up, your U.K. automatic-only license serves as a provisional for driving a manual car, so on the 366th day you would then be required to conform to all the other requirements for a British learner in the same position: "L" plates, accompanied by a driver at least 21 who has held a U.K. license for 3 years or more, not allowed on motorways, etc.

I'd also like to ask, for insurance purposes, does it matter if I have been driving for 10 years in the USA? Or is it, as far as theyre concerned, I am a new driver since I just got my British licence this year?

They vary.  Some seem willing to accept a U.S. driving record to give you a no-claim discount, others don't.  As with everything to do with car insurance, it really pays to shop around and play them off against each other.