One of the things that Jacob Lurie finds important is to "think invariantly": Do not use model dependent definitions. Do not prove model-dependent results.
Here's an example to illustrate what I mean:
"The $\infty$-category of spetra is the free stable $\infty$-category with colimits generated by a single object".
That's a nice model independent definition of the $\infty$-category of spectra.