You shouldn't be grabbing, anything.
I realise it's probably only a word, but even using the word means you are more likely to be grabbing rather than smoothly building up the pressure on the lever...
But yes, use the front brake and don't worry about the back for "general" braking (especially as yes, you do have linked brakes

). The back brake comes into it's own at low speeds and on loose surfaces, plus a few other "specialist" applications such as mid corner tightening of lines etc.
If you choose to do any further training, you will also get taught it's advisable to brake first then change down rather than do at the same time, or change down to slow on the engine...