Advice for new cyclist?

What bike did you get? If you plan to use as a commuter, you need a good U lock. Don't leave it outside overnight ever, regardless of whether it is locked. Thieves can break the best locks if they have enough time. I am kind of paranoid about bike theft, so maybe not the best person to ask about the issue, but be wary of leaving a shiny new bike out anywhere, even locked for too long, as newer bikes are theft magnets.

If you plan to ride in rain, you should mount fenders. And you may want to get a rear rack for carrying stuff. I know you can always use a backpack, but spreading the weight of the stuff you have to carry will reduce fatigue on your shoulders.

Do you have helmet? How about a good floor pump? Bike tires should be checked at least weekly as they do lose air quicker than car tires, and unless you live right next to a bike shop, you need to be able to pump up your own tires.

What is the longest you have ridden? What are your goals in this regard? I have more thoughts, but need you to be more specific with your questions.

Giant makes a quality product, so good choice.

As far as racks go, maybe your bike shop has a few, but something like this is what I have in mind. I have these kind of racks on several of my bikes.
http://www.nashbar.com/bikes/ProductDisplay?storeId=10053&langId=-1&catalogId=10052&productId=552297&utm_source=Google_Product_Search&utm_medium=pla&utm_campaign=datafeed&cm_mmc=Google_Product_Search-_-PLA-_-Datafeed-_-Topeak Explorer Tubular Rack&CAWELAID=400006960000028659&catargetid=1572651360&cadevice=c&cagpspn=pla
http://www.outsideoutfitters.com/p-2775-planet-bike-eco-rear-aluminum-rack.aspx?variantID=7286&gclid=CPOhhJThjrgCFbFAMgoduSEAvQ
http://www.amazon.com/Axiom-Transit-Tubular-Alloy-Black/dp/B001GSQUU4/ref=sr_1_3?ie=UTF8&qid=1372697674&sr=8-3&keywords=axiom+bike+rack

And for commuting or day trips, you can mount a bag like this to the rack. http://www.nashbar.com/bikes/Product_10053_10052_167746_-1___202599

Once you get into things more, you might want to consider getting some cycling shorts, which will increase your comfort on long rides, because of the compression, and because the tight fabric won't bunch up and chafe, and cycling shorts are designed so the seams don't irritate you as you ride.

Stay off the sidewalks, and always ride on the correct side of the road. No one likes a salmon swimming upstream in traffic.

You’ve had a lot of good advice but as in life make sure you enjoy the ride. I started at 15 miles a week for exercise and loved it, felt like a kid (I’m 61). I now do 130-150 per week with two 30 mile + “adventure rides” each day of the weekend. I’ll eat, shop (love farmer’s markets) trail ride and just goof around 3 to 5 hours sometimes. I don’t consider it exercise just fun.
As time goes you’ll decide what you need as far as accessories & even what bike you end up with. Take your time don’t rush out & get stuff you’ll never use. I know this is sacrilege to many (& I’ll hear about it) but I don’t wear a helmet unless I’m on very,very busy streets. There uncomfortable for me & in my mind the stats don’t support it. If you feel better with one by all means wear it. Most of all have fun & enjoy the ride.

Gel saddle

Not necessarily. If OP's saddle is comfortable, I say stick with it. Saddles are a personal thing. Fit is more important than how soft and squishy it is. And fit is really a personal thing. I used to use a saddle with springs to dampen the vibrations. It was very comfortable. Then I tried a gel saddle, didn't love it, though I put it on my wife's bike and she liked it, and still uses it. Now I use a leather Brooks B17 saddle. Most comfortable saddle ever, but it is by no means soft.

Soft saddles are bad, because they compress soft tissues/nerves that shouldn't be compressed. Basically, you want to sit on your bones, not your meat!

That's why endurance cyclists have hard saddles and specially designed chamois.

Gel saddle

Not necessarily. If OP's saddle is comfortable, I say stick with it. Saddles are a personal thing. Fit is more important than how soft and squishy it is. And fit is really a personal thing. I used to use a saddle with springs to dampen the vibrations. It was very comfortable. Then I tried a gel saddle, didn't love it, though I put it on my wife's bike and she liked it, and still uses it. Now I use a leather Brooks B17 saddle. Most comfortable saddle ever, but it is by no means soft.

Soft saddles are bad, because they compress soft tissues/nerves that shouldn't be compressed. Basically, you want to sit on your bones, not your meat!

That's why endurance cyclists have hard saddles and specially designed chamois.

and this ^ softer seat doesn't mean better,

Get yourself a copy of Zinn and the Art of Road Bike Maintenance (some small differences between commuter & road bikes) and learn how to look after minor repairs yourself.

Keep your chain, rear derailleur & cassette (gear cluster) squeaky clean (not too much oil either). Dirt buildup leads to premature wear and inaccurate shifting.

If your commuting invest in decent lights for your bike. I have a white LED blinking light on the front (and use it on all my rides) as my "see me" light, I also have a more powerful light for riding at night as my commute includes unlit bike paths (sorry to sound sexist, not something I'd recommend for a female cyclist riding by herself) and I have a red blinking LED for the back of my bike (Planet Bike SuperFlash) which I also use for all of my rides. Wear bright, high visibility colours (or a safety vest if you're riding in street clothes) and ride defensively.

Have fun and ride safe!