I think @toddl1985 's advice is also solid: don't take it too far early on.
In the beginning you won't get great parts from the high heat races anyway, so just bump it until 1 or 2, maybe 3 then call it a night. Keep banking that rep until you can afford a decent car with decent parts.
Another few tips:
A nimble car is better than a fast car. I'm using the Exige S which is dirt cheap at 77k, an engine swap costs a measly 81k and it tops out at 373 kmh when fully tuned and lowest downforce. It's extremely nimble so very easy to lose the cops in the city area and it's also great at dodging traffing. Porsche 918 is great for this purpose too. Might be others but haven't tried most of the cars yet. :P
Use the radar disruptor to make evasion easier. I combine it with the repair kit, so I have a total of five repairs (three from gas stations and two from the kit). Use the gas stations first, save the repair kits for when you really need it. My runs end when I'm out of repair kits.
Last but not least: letting go of the throttle and using the brakes (including the handbrake) can save your life. Yes, this is an arcade game, but that doesn't mean you can just floor it all the time, there are mechanics. And each car behaves differently so pick what suits your style.
Night races are good fun, the cops follow a clear set of mechanics so once you know those it becomes pretty easy. Same for dodging traffic. Learn the patterns.
