There is a lot of overlap, but you certainly should be ready to use the full range of gears.
Here’s what I do:
I usually start out on my small chain ring. If I’m going up a hill or I know I will not want much speed, I might stay there for a while. In a race, I usually go up to the big ring pretty quickly. With the small ring, I only use my first 4 or 5 (out of 11) cogs—the largest ones. And with the large chainring I only use the eight or nine smallest cogs. Because of the overlapping ratios, there is no need to ever be in a largest-largest or smallest-smallest combo.
Unless I’m pulling a trailer or starting out on a steep hill, I start on my third or fourth largest cog and work from there, often going to the fifth or sixth pretty soon, along with shifting up to the large chain ring.
I seldom use my largest cog, but I’m really glad it’s there for the steep climbs I occasionally encounter.
I likewise seldom use my smallest or next to smallest cog, only if I’m descending a steep hill and really feel like pushing.
Therefore, most of my riding is on either the small chain ring and the second, third, or fourth cog or else the large ring and third through ninth cogs.
On my bike, it is easiest to shift down to the small chain ring when I approach a stop and know I’ll want a lower gear to get started again. Once I’m back up to speed, I can easily go back to the large ring. This works better than shifting two or three cogs for the equivalent ratio change I desire in this situation. Shifting up or down one or two cogs is for fine tuning my cadence while cruising.
In a race, I will likely be on the big chain ring most of the time, but I dang sure go to the small one when there’s a steep hill to climb, and if it’s very steep and/or long, I might also be on my largest cog.
Google Sheldon Brown Bike Gear Calculator, put in your parameters, and it will generate a nice little chart showing all your ratios. You can look at gear inches, meters development, or gain ratios. You can also see your speeds at various cadences.