Before you do ANYTHING else, the FIRST thing to do is to dial in the springs.
Race Tech has a chart that will give you an idea as to what spring rates you need, then you get to decide if you need new springs or not.
Try to set the sag and see what it looks like. If you need HUGE spacers, or have to crank the preload to the top or bottom, you probably need springs. I want the sag at about 33-35% of the travel, if you can't get close to that you need springs.
You can get acceptable suspension with the stock parts... except for the shock... it's 15 years old and wasn't very good to start with. You can refresh the shock, and then you'll have a nice fresh piece of crap shock. There are lots of bolt on solutions, BUT if I was going to spend a nickle on the rear shock I would be replacing it with something 6 way adjustable Ohlins, Ktech, Penske, Fox or Maxton (if you get one used have it refreshed: new oil and seals, check the bladder for holes, recharge the nitrogen).
Inspect and service all the pivots, the swingarm pivot and linkages and the steering head bearings.
The forks need new seals, sliders and oil.
Emulators are nice, BUT all they really do is make tuning easier... sorta.
In non cartridge forks, like stock SV forks, the compression is controlled/tuned by the area of the holes in the metering rod.
Too much compression> make bigger holes
not enough compression> make the holes smaller.
The rebound is controlled by oil viscosity.
Too much rebound> use lighter oil
Not enough rebound> use heavier oil.
With emulators you make the holes so big they do nothing and the oil is metered though the emulator, which is a poppet valve tensioned with a spring.
Swapping a Gixxer front end on a SV is a fairly simple task, but they're usually shorter so you'll lose some trail. Not all Gixxers had cartridge forks. Swapping in Gixxer non cartridge forks is no gain.
They've been racing SVs long enough now they've got it figured out