SV650S is a great choice for a fairly novice rider
I bought a 1999 SV650 as my first street bike after about 15 years away from bikes. I had several years of dirt riding experience, but none on the street. The SV650 and MSF RiderCourse got me going in a safe but very fun way. I now have a 2002 SV650S and like it even better.
I hesitate to recommend the SV to anyone with absolutely zero riding experience because the low end torque can get the bike ahead of your brain very quickly if you're hamfisted with the throttle. A careful person would probably have no problem with it after just a weekend MSF RiderCourse, and 28 year olds are, in general, more careful than 18 year olds. In your case it should be no problem at all. The new 2004 with lower seat will be better for shorter riders, but at 6' that probably won't make any difference to you. In fact it may be worse if they didn't lower the pegs along with the seat.
The SV doesn't have great suspension as sportbikes go, but compared to a Shadow Spirit it's probably considerably better. The cheap fix for the forks is to turn up the preload and use thicker oil to better damp it. The shock you're just gonna have to replace eventually. A Fox twin clicker or Traxxion Dynamics' Penske "sport shock" are the best bang for the buck. If you want top notch, go with RaceTech emulators and springs in the forks and an Ohlins shock. Changing exhaust is really for sound, 'cause you're not going to get much more out of the excellent motor. If you decode you need more braking power, EBC HH pads up front are great, and cheap, too. A Zero Gravity sport touring windscreen helps with wind protection. If you're wearing a 3/4 helmet behind a "Roman shield" windscreen on your Shadow, you're going to NEED a full face helmet.
Great choice! I've also owned a 1998 VFR, 2000 Sprint ST, and 2002 Bandit 1200S - all great bikes, but I still love my 2002 SV650S and it has a permanent place in my garage...