The GFCI (aka GFI) protects against unbalanced electric flow. This is one of the greatest leaps in personal safety technology to be widely available and deployed. It is now very inexpensive (<$16) to protect a whole circuit.
No, the house is not in any danger from having non-GFCI circuits. It is 99.9% a personal safety issue. If a device you are using somehow fails and delivers some current through your body—instead of through the electrical circuit—the GFCI detects this circuit imbalance and, within 1/20 of a second, "trips" and stops the shock.
Sure you can forego upgrading your outlets. Your garage probably has only one or two circuits, so you can save $30. Or if you would have to hire an electrician, you can save $120 or so.
To me, having GFCIs is a great value. Unless you and all your guests don't use electrical devices, it is excellent peace of mind knowing they won't be shocked. Of course they can still accidentally drill their limbs, burn and drop heavy stuff on themselves so a garage may not be a first to incarcerate teenagers....
As far as DIY work, replacing an outlet is 1 or 2 of out a possible 10 in complexity:
- Turn off the circuit
- Verify the outlet is dead: plug in a known working portable device (radio, light, hair dryer, etc.)
- Remove the cover plate screw(s)
- Loosen the two screws holding the outlet in.
- Pull outlet out, stretching the wires to a convenient working position.
- Notice the wire color pattern. In North America, it should be black wire to bronze connector, white wire to silver connector, and bare (uninsulated) or green wire to the outlet frame. If not wired this way, check other outlets with an $8 outlet tester.
- Remove wires from old outlet. There are two predominant fastening means: screws on the sides or "quick install" holes. For the quick install holes, there should be (another) small hole where inserting a narrow screwdriver or carpentry nail makes it release the wire. Failing that, you might be able to muscle the wire out with a forceful quick tug. Or just cut the wire.
- Prepare the wires and connect to the new outlet. If using the screws, make the wire go in the direction the screw turns when tightening. Otherwise tightening will push the wire out from under the screw head.
- Test wire connections mechanically by tugging firmly to make sure they won't slip out.
- Fold and push wires into box so they stay out of the way. Be sure the bare wire is fully in the back and nowhere near the sides of the outlet, except where it is screwed to the outlet frame.
- Push outlet into box and tighten screws.
- Install outlet cover.
- Turn on circuit.
- Insert tester into outlet to verify correct wiring.
It may seem like a lot of steps, but it is quite simple.
By the way, that button on the outlet tester puts a small load (0.01–0.03 amps) between the hot wire and ground. That will trip a correctly working GFCI. If the circuit has no GFCI, pressing the button won't do anything.