The gearing doesn't influence how much power the engine has or its enhance ability to engine mods - but it does have some bearing on how that gets translated to power applied to the ground. But even in that regard, a very small fraction of that power "gain" will be realized between the A131L 3-speed auto and the A245E 4-speed auto - given that both are automatic transaxles, in fact, between the two transaxles, their effective gearing in the first three gears are nearly identical. Even if you had a 6-speed automatic, the amount of power gain that is translated to the ground will be minimal. Swap in a 5-speed or 6-speed standard shift, and now realize a greater fraction of the engine power going to the ground - given the greater drivetrain efficiency, inherent to a standard transaxle, and lower weight (roughly 1/2 the weight of a 3-speed or 4-speed).
Top speed and highway RPMs, on the other hand, is the one that is most likely to be affected more than engine power. Gearing and tire height all contribute to top speed. The taller 4th gear allows the engine to turn lower RPMs at cruise, improving highway MPG. Though acceleration to get up to that speed is another matter, depending on gearing, you could build a 3-speed out accelerate a 4-speed up to a certain speed. To maximize how much power you can put to the ground, you have to "match" the gearing to the powerband of the engine.
Brands for suspension, tires, wheels, and brakes - really depends on what you are going for and your budget. Especially with suspension and wheels - you can go mild to extreme.
My current setup is as follows:
- 14" light allow wheels (~10lbs)
- 205/60R14 Bridgestone Potenza RE960AS Pole Position tires
- plain Brembo rotors, OEM drums in rear
- Hawk HPS pads up front, OEM shoes in rear
- TRD springs
- KYB GR2 struts
- OEM rear trunk brace
Car exterior stays stock, sits about an 1"-1.5" lower, PLUS 0 tires on those particular wheels pushes my F/R track out a bit compared to stock. But handling and braking are greatly improved over stock, performance improves just a hair - while retaining all the original reliability of the Toyota Corolla.
From your pic - looks like an EVO 1 body kit running on 16" or 17" wheels. A good start - I'd recommend getting the front fogs/driving lamps coated or otherwise protected. Even though the sit pretty high up, lots of owners had theirs cracked/chipped by normal road debris.