I am no expert on what to buy... How about an Apple laptop?
I am a big fan of HP laptops. My first gave me no trouble for a year and half (at which point it was struck by lightning, which was not HP's fault); my current one has given me no trouble period.
Before an anti-Mac fanatic answers I will. Apple's laptops are not immune from this exploding battery either. An Apple iBook G4 burst into flame after being left on by an 11 year old boy a couple of months ago.
He did leave it sitting on a shag rug on the floor which may have impeded the cooling airflow, but it did indeed burst into flames.
Also the initial production run of Mac 5300 laptops was prone to overheating and some of them got hot enough to warp the plastic case. The problems were traced to a Korean battery manufacturer. 28,000 Mac laptops were recalled for battery replacement. At the same time, 129,000 HP laptops were recalled because of battery overheating... the batteries were manufactured by the same Korean company that was cutting corners on specs.