Recommended Modifications for Racing
I get this question a lot so figured I would put my thoughts here.  These recommendations are based on someone who wishes to race.  My experience is based around endurance desert racing, and grand prix WORCS style racing.  The first thing I recommend is entering a race with your quad without dropping any money on modifications.  You really should try it out before you drop 2 grand on a suspension.

General Tips
The key to getting faster is confidence and conditioning.  The first item, confidence; you don't have as much control over.  I say confidence because your "speed" over or through an obstacle is all about having the confidence to know that you can fly through it and you know what you and the machine are going to do.  This comes from experience, skill, and comfort.  

The second item is conditioning and it is just as important.  You have 100% control over your conditioning level.  If you are in shape you will be a much faster racer, this is obvious and no one can argue this.  Your conditioning will increase your comfort level which will allow you to be much faster and go through terrain with more confidence.  I have also found that when I am in great shape the entire race is much more fun for me.  I am not being punished and feeling the burn in my arms, legs and lungs because I am in shape.  So I am having a great time during the race and focusing on just having fun.  Of course it takes 40-200 hours of punishment in the gym in order to experience 3 hours of joy during a race.  The only way to succeed in any form of racing is to get yourself in shape.  I went from the Beginner class to the Open Expert class champion within one year by getting in the gym.

ATV Modifications
I will try to order this list in the order I recommend your purchase the parts.  In the end it is all about being comfortable and confident on the quad so the order might be different for you because you have problems with  your hands so you buy the FASST bars sooner.  I believe any expert to pro level race machine will end up with all of the stuff on this list eventually.

1.  Setup your stock suspension, set your tire pressures, do the "free mods" and go racing.
Stock ATV's are marketed and built for people of all shapes, sizes and ability levels.  If you suspension is adjustable, adjust it for your weight and
riding style.  Many ATV's have some free or cheap things you can do to increase horsepower.  Research these things on the internet and go for it.
These things typically include air intake and exhaust modifications that are cheap or free.  If you enjoy racing then proceed to step 2.

2.  Good rear skid plate.  For desert racing you will need a decent swing arm skidplate.  The stock plastic one isn't good enough for a desert race.  PRM, Pro Armor, and AC Racing all make great ones.

3.  If you enjoy racing at the beginner to intermediate level next up is the suspension.  Send your shocks in to get revalved/resprung for your body weight and riding style.  I recommend GT Thunder racing.   On a Honda this includes getting a new rear linkage.

4.  Wider a-arms, wider axle.  I'd recommend doing the a-arms and shocks at the same time because the shock tuner may adjust the valving a bit based on your a-arms.  I recommend the JD Performance a-arms for their durability, customer service, and easy caster adjustment.  For the rear axle I recommend Lone Star Racing or RPM Dominator.  Many new atv's today already have wider a-arms and axles so this step is already done!

5.  Desert seat.  If you are big and lazy like me you probably sit a lot when you race.  My quadtech desert seat is one of the best mods I have ever done.  I purchased the install it yourself seat kit which took a good 2-3 hours of stapling and pulling to fit.  If you have the means I recommend buying their installed seat cover and seat pan.  Or buy the DIY kit and pay a local upholstery shop to install it.

6.  FASST Flexx bars.  Great for reduding arm pump and vibration.  Can also raise the bars up a bit which might be required after installing the desert seat.

7.  Precision Steering Stabilizer.  I have heard the Elka is good too.  I don't believe much in those cheap shock style ones but that is just me.  The stabilizer will help keep the bars straight, might help you out of some scary spots if you get out of control and generally make you more comfortable.

8.  Engine.  By this time your stock engine probably needs a rebuild.  Throw a 12.5:1 or 13:1 piston in there and get an aftermarket cam.  If you want even more power have the head ported too.  Keep the compression under 13:1 for desert racing.  The higher comp isn't worth it, I have tried it.

9.  Wheels and tires.  Your stock wheels and tires are probably shot now.  Get a set of Maxxis RZR II's for the desert.  I run 20" rear and 22" front for all GP courses and even practicing at the mx track.  For traditional desert races I now use 22" rear and 23" front but you can easily run 20/22's for any desert race so don't feel stressed if you don't have a set of 22/23's.  Of course if your quad came with 18's from the factory then you probably need to get a set of 20/22's a lot sooner than this.
Wheels- the stock wheels (at least on the honda) are pretty stout.  We used them on the Baja 500 race quad in fact.  For aftermarket wheels I can't say enough about the Douglas Yellow label ultimate beadlocks.  Mine have been tremendous.  I didn't have much luck with ITP beadlocks.  My front wheels are Hiper Tech 3's and they still look brand new even after 18 months of racing.  Make sure you get the Tech 3's and not the all carbon fiber cheaper versions, they will not hold up to racing.

10.  Bigger gas tank.  IMS and Clarke both make gas tanks and both have good customer service.  Dry breaks are nice on race day but really a PITA at other times.  You  need a special can or adapter to fill them and they seem to leak a lot, at least in my experience.  Stay with a traditional tank as long as possible.

11.  Not much else to do, maybe bumpers, full chassis skidplate, fancy levers, hand guards or maybe more power with a stroker kit.