There are a lot of options here for upgrades and room for improvements.I will list each with my opinions and experiences.I will start with the most expensive option first and work down to the least expensive.
$695 Works piggy back street shock offers non adjustable dampening,but does offer adjustable preload.Pretty much a stock shock with better valving and you can chose a stiffer spring.Better options on the used market.I'm not real familiar with this shock.I don't know if it changes the height from stock.
$150-$500 Cannon Race Craft will re-spring and re-valve your shock, and work with you to get the proper spring rate for your application.They will rebuild and modify shocks upon request.Ask for Tony.Even tho the GS shock only has preload adjustment,Cannon should be able to re-spring and re-valve the shock to match any upgrades done to the front suspension.This is an option for someone needing a new shock that wants a no fuss set up that's better than new.This set up will not raise the bike up,unless the shock was sagging from age and wear.
$50-$200 2006+ Yamaha YZF6R AKA R6 rear shock.These can be rebuilt with Race Tech springs and valving for a super performing shock.These are completely adjustable right off.Very few will feel the need to build their shock for better performance.You need the shock with the clevis on the bottom,along with the bushing that goes through the linkage,and bolt.The red spring has a rating of 9.8kg/mm and the yellow spring has a rating of 10.1kg/mm.Not really enough to make much difference.I say go yellow if you can.This shock may raise the rear about an inch.This is usually due to an old sagging shock or old badly adjusted original shock preload.
$40-$120 Suzuki SV650 rear shock.You need the standard shock without the fluid reservoir.The clevis end has to have a new mounting hole drilled and the excess clevis has to be cut off.This is not really difficult but a beginner mechanic should weigh options carefully and seek help.I don't know the spring rate difference between colors.Here is a write up on modifying the shock to fit.Be aware that this shock can raise the rear up a couple inches which can cause the steering to quicken dramatically.This may cause a new rider to crash.
$15-$80 88-97 Suzuki GSX600/750F Katana rear shock.This is the shock I have.It has preload adjustment and rebound adjustment.It will raise the rear about 1 to 1.5 inches in the rear.This depends on preload, and how bad the old shock was sagging or adjusted.These shocks are getting hard to find in good usable shape.They can be rebuilt but you have to find a very knowledgeable person to do the work.That gets expensive.
If you install a shock,and it's too high,you have options.No need to remove a shock upgrade because of the height.You can get lowering links fairly cheap.Most will get 1 to 2 inches of drop.That will more than compensate for the shock's extra lift.They are easy to change.Suspension links are the same from 1989-2011
Yana Shiki 2" Drop Billet Aluminum Lowering Links
GS500 Lowering Links
Burkhart Cycle 1 to 3 inch drop links