Being realistic a 1.0L Toyota Yaris 1999-2000 and onwards would be your best bet. You can make them look quite smart. If you can afford a brand new car, a 107, C1, Aygo, Corsa 1.0, Peugeot 208 1.0, or Clio 1.2.
The engine size does play a part in insurance but its not so much to do with the engine as you would think. My 17 year old brother is currently insured on a Peugeot 206 GTi HDi 1.6, with 110horsepower standard, 0-60 in 8.5~ seconds. And generally a really quick car, his insurance is £1200. Yes this is expensive but I wouldn't expect to pay too much less on a first car.
The majority of the reason for high insurance is the area you live in and the type of car you choose, the cars you really wouldn't want to drive as a new driver are really cheap, and the cars you do are a lot of money. This is due to the fact insurance companies look at statistics and see how many cars have claims ran through on them, and populate what cars are the biggest risk. The best way is either a really uncommon car, or a brand new car - as insurance is much cheaper, but then again the car is very expensive.
I am currently 21 and have paid over a thousand pounds for my insurance almost every year. My cars have ran, with insurance premiums;
1st year driving: 2003 1.4 Diesel Fiesta £2,300
2nd year driving: 2004 2.0 BMW 3 series £1,200
3rd year driving: 2005 2.5 BMW 3 series £950
4th year driving: 2007 3.0 Twin Turbo BMW 535d: £1,300
It is illegal on your insurance company to have yourself as a named driver when you will be driving the car the most, which is most likely. It is legal however to add on other drivers who may drive your car, for example my grandmother and grandfather are insured on my policy, but I have declared they have their own vehicle which they drive and will drive my car rarely (never!).
Make sure you chose your car wisely. I have insured with a company called bell.co.uk (part of admiral group) from when I very first started driving and have found them the cheapest (and very, very good) by far. They now have a new option to install a black box to your car, which monitors how well you drive and significantly lowers your insurance. As well as this your insurance will continue to lower in future if you prove how well you drive!