If you've never been on a bike, the best way to start is to take the Motorcycle Safety Foundation Beginning Rider Course. This course is offered by junior colleges and municipal recreation departments. It's a two-day weekend course that includes a day of classroom instruction and a day on a closed course learning from scratch how to ride a motorcycle. And best of all, they provide the bike (usually a 125cc or 250cc model). If you successfully complete the course, many states will waive the riding portion of the test for your motorcycle license endorsement. This is the best way to get started with confidence. Then you can go shopping for your first bike.
Both of these are good bikes. I haven't ridden the newest iteration of the GS500, but I recall the ninja having more motor. Really you should be able to live with both bikes for quite a while, but neither of them are likely to high side you if you're careless.
Take the safety class, buy the bike that appeals to you. Either one should be relatively maintenance free, check insurance rates, you may find the Suzuki cheaper to insure. Buy the one that stirs some passion in ya.
There's a suggestion above that you take the MSF before purchasing any bike, which I strongly second. The MSF is a great way to get a little seat time and some good information.
After taking the MSF, I'd look at which bike fits your budget better - remember that things like (good) gear can be a little pricy (but worth it). If you're looking at the GS500 series, you might consider the unfaired GS500 as an option - easier maintenance access and cheaper when it gets tipped over in a parking lot/garage/whatever (seems to happen alot - I managed to tip my first bike over in my driveway on the day I got it).
If you're absolutely set on a 500cc faired bike, I'd suggest the EX500. It's been around forever, seems reliable and the few reviews I've seen that have both bikes seem to prefer the EX500... I personally have an EX250 (I also had one as my first bike, sold it a few years later and immediately regretted it - I ended up acquiring another one...), which has been an excellent bike and I'd certainly suggest that you consider that as well - it's held up as one of the premier 'beginner bikes' in a lot of places, and although many folks will tell you you're going to 'out-grow' it, I've found that the more I ride, the more I appreciate still having the Ninjette around...
Spend $1500 (or less) and buy an old CB750. Doesn't matter what year. Ride for 6mos putting at least 3000 miles on it. then decide if you like riding enough to invest more. And take the MSF course. You'll be glad you did.
a CB750 is NOT appropriate. It's too damn heavy and genrally suffers from iffy brakes. It was my first bike and I rode 25K miles that first year so I've been there and done that. I got a pair of GS500e's later (road and race) and the grin factor was HUGE!
Personally I like air-cooled motors - they are so simple. the EX has more power for sure (like 10HP) but the GS is a blast. Find a nice late 90's example and they'll be rather cheap.
I have ridden neither one. However, I do own a EX250 and have about 15000 miles on it. It is small but it has its charms. I think it is mostly about price, ergonomics, and power preference. The EX250 goes about 27 hp, and I think the gs is around 35, the EX500 is around 50. These 3 bikes have stood the test of time, and I think they are all good bikes for beginners.
One of my first rides was an excellent 82 model. No iffy brakes, completely reliable. The only difference between the EX and the CB is the number of cylinders. The bikes are within 25-35 pounds of one another in wet weight. And $1500 is way better than $3000 if you don't know what you want to spend money on. He could find a perfectly reliable 82-84 Nighthawk and ride for years before moving to a different bike. If he were really clever he'd look for a Honda Hawk 650. Light, fun, great mileage and he can turn it into a club racer when he gets some time in the saddle.
BTW, there's no rule that you have to "outgrow" your first bike and get rid of it after a few years. My first bike was a Yamaha Maxim 400 (air-cooled parellel-twin cruiser) and I rode it with a grin on my face for 12 years. I think you could be quite happy on either of these bikes for a very long time.
a: Get a Ninja 650 or SV650, and practice right wrist discipline. At low RPM, the 650s aren't that much more than the EX500, but is a much better overall package. I WISH I started on an SV650 instead of an EX500, i'd still have the SV... THe Ninja 650 is especially good because it is very narrow, has a really low CG, and has a very low seat height.
b: Get an EX250/Ninja 250. Its fast enough for the freeway, very VERY light and forgiving. And when you upgrade to a bigger bike, you either sell it for almost what you paid or KEEP the 250 as a commuter hack/trackbike, as its light weight, tossability, and low cost make it a much MUCH better track bike than an EX500.
In retrospect, I wish I did one of the two options instead of getting the EX, which was a great bike but I replaced it in 2 years with a VFR.
i rode a fzr600 for my first bike (not a great choice) but i survived with a few close calls and nothing more than a couple tip overs while not moving. i have not ridden the EX500 but i had to sell my fzr and my wife bought a gs 500 with fairings after taking the msf course i now ride it and like its quite peppy up to 60 but is buzzy and the mirrors vibrate like crazy. but it corners well enough is predictable and also difficult to get yourself in trouble with. id reccomend it ps also can get 55mpg if your not too much of a speed demon. i do believe the ex500 is suppose to have alot more in the performance area but as a beginner it would be a little bit before you could get all the performance out of either of these bikes