Don't despair too much.

It's my opinion that entry level equipment like yours and mine lacks consistency more than potential. I've had a handful of shots at home that were reasonably close to best, and quite a lot that were tasty.
The biggest problem with your machine, as you've indirectly noted, is temperature consistency. There's just not enough metal on your Gaggia to compare to a thermal titan at Intelligentsia. Your boiler comes on because it needs to keep up with the cool water entering it. But that doesn't necessarily ruin the chances of a good shot.
If I had to guess, I'd say your problem is with distribution. That's what I struggle with the most. Very small inconsistencies in the puck can cause channeling. channeling messes up flavors, blondes espresso early, and is hated by espresso enthusiasts everywhere. Higher doses mitigate the problems associated with bad distributions, but they don't solve them.
Do a search for the Weiss Distribution Technique (WDT) and think about some of the discussion on it. The next most common advice is to get a naked portafilter and examine how the espresso comes out of the screen.
This article from the FAQs shows the diagnostic possibilities of naked portafilters.