Ok...although I'm no expert (maybe John Coffey will pipe in), I self taught myself over the years, so take this advice as such:
1. Concentrate the weld pool on the thicker material and 'dip' onto the weaker material.
2. Weld in shorter bursts to decrease the heat in the metal.
3. If there are gaps where it is diffucult to shape the new metal to the old, weld up to the point where the gap begins, then, while the metal is still hot from welding, hammer it into shape so that there is a good meeting of the two metals.
4. Take your time. You may need to do it as little as a small 'tack' at a time to prevent burn through. You'll find that once it has some weld material, it will be easier to run a second pass to get good penetration....but this only works where cosmetics are not too important...
Tim
[edit] Flux core is not stronger. The gas is used to shield the weld from atmospheric impurities (oxygen). Gas shielding is usually better, neater and stronger. That said....all my welding was done with flux core wire[/edit]