We opted for a Powermax+ from Visonic.  I believe its the same system BT sell with their name on it (if you want monitoring). I'm not sure if BT will take over monitoring of a DIY installed visonic system though. They may want it all professionally installed.

We're using five of their "Quad" series wireless PIR sensors because I heard they were very imune to false alarms. Seem to work well. No problems over two years and still on first set of batteries in the PIRs. They also have a cheaper range of PIR sensors but not tried those.

Also have some wireless key fobs so no need for keypad in the hall. Just arm and dissarm like you do your car.  

Apart from the bell box that's all you need to get a basic system working.

Our phone line is buried in the ground so we use that for comms. Whenever the system status changes it calls me up on the mobile and talks to me. The messages it sends (or not) are configurable. You can also get a GSM modem which allows it to send you SMS messages instead of voice calls. We haven't bothered with one of these. Our phone line is burried so can't easily be cut.

Visonic don't really intend it to be DIY installed but it comes with an installation manual. Pretty complicated but mainly due to all the features - 99% of which we aren't using. For example it's possible to have some sensors enabled at night with others disabled so you can walk around without setting it off.  

In the UK you have a choice of frequency bands. 434MHz and 868Mhz. Allways check when buying add-ons that they are the right band as some sellers don't specify the band on their web sites. I opted for the 868Mhz band because I think a lot of garage door openers and the like use 434MHz (or is that 433mHz). However 434mHz kit seems to be more readilly available and I'v not heard of any problems with garage door openers.

Home page
http://www.visonic.com/VisonicHomePage.nsf/homepage?Openform

Rather dated review..
http://www.automatedhome.co.uk/Security/Visonic-Powermax.html

Several suppliers in the UK of kits and add-ons. See also ebay.

Edit: I'm not familiar with other makes as I'm not trade. Just a happy user of this one.

I would go for a Texecom Veritas Excel, a tad more than the R8 or PLUS, but worth it.  Fit this along with a Texecom speech/text dialler.  (also sends SMS texts).

Look at http://www.securitywarehouse.co.uk/catalog/index.php - They do all the kit cheaper than my local wholesaler does, with the exception of the cable.

You should get yourself a panel (which includes the keypad), battery, bellbox (and cover, they are sold seperately for the Texecom ones!), an internal speaker, some PIR's and magnetic contacts for the door you intend to use as means of entry/exit (preferably).