A lot of circuit breakers work because they have a bimetallic strip inside (a strip made of two different kids of metal).
LNK When the breaker is overloaded, it heats up, the different metals expand at different rates, and the strip changes shape, opening the circuit. (sort of like going from a C shape to an I shape, or vice versa)
Because of that, after they've been popped a lot, they can REALLY lose their rating (the metal inside weakens) and they'll pop if there's a sudden surge of current. (like your computer starting up).
SO that's why I'd say #1 probability is a bad breaker. Assuming, of course, that your home doesn't have wonky wiring. I've seen a lot of older places where the home-owner has added onto the electrical system him/herself and there's a set of lights in an addition that are on the same circuit as the fridge plug, for example. My dad's house has the outside plug on the same circuit as the kitchen. My brother's trailer has kitchen lights on the same circuit as the plugs in the spare room, the lights in the addition on the same circut as the hallway, and the plugs in the addition on the same circuit as the bedroom. Of course, with a completely unlabeled panel box
If at some point you CAN have an electrician come and trace your circuits, it could find out if that's a problem, but it'd likely be expensive, so that's a last resort.
#2 bad wiring, #3 is probably bad receptacle or bad contact between the receptacle and plug, or loose wiring on the receptacle.
I'm not an electrician, either, so take my advice with some salt.
How much do new breakers go for though :/ and wouldn't an electrician need to install it or is changing the breaker simpler than I think?
$5-$10 for a standard 15-amp. Don't buy a larger breaker than what's originally in there, as the circuit will be wired to handle what the breaker is. No, strictly speaking, an electrician doesn't
need to install it, but unless you know what you're doing, I'd REALLY suggest having him do it.
Also, What 95Viper just posted.