I agree that starting out slow and going for consistency and then speed is a good way to go. What I imagine you're doing is trying to improve lap after lap, setting faster times as often as you can. Instead, just set yourself a goal time to stay under. If you're fastest lap on a track is 1:06.00 (for example), don't try and match or beat this every lap. Just try and stay under 1:07 for a handful of laps. If you struggle with this, then just aim to be under 1:08 for a bunch of laps. Once you're happy doing this, then try and go back to pushing a bit harder to try and stay under 1:07.
Another important thing I find is knowing where I can push harder, and where I am already going as fast as I reasonably can. When you want to try and improve your laptime, it's important to know where you can pick up speed. If you just try and speed up everywhere, you'll likely go over the limit at some point and crash. The more aware you are of your limits and how close you are to them at different points on the track, the better.