Hi welcome to the forums and congrats on your new car... Now for your questions.
Yes you will need to get the cars computer tuned for the new gears, the car still thinks it has the stock 3.27's in it and the speedometer/trip monitor will climb higher than normal... When I got the gears installed on the car I waited about 5-6 months till I bought a tuner and racked up more mileage than it does have right now, but I plan on keeping this car for as long as I can so mileage doesnt bother me... When it was not tuned I would go about 275 miles in the city and I thought this isnt right I cant be getting 22mpg in the city! Then I learned that I had to get it tuned...
You should be able to find a tuner shop in the area to get the computer tuned but its going to cost a lot because your basically buying a dyno tune and that can get pricey by the hour, but if you have a lot of boltons or other power adders this would be a good time to get the car tuned to get the most hp you can get it out of it vs a mail order tune like I have.
Me I went the other way and bought a SCT X3 Tuner from American Muscle and I love it for what it is. I was happy to just get the speedometer reading correctly, but the mail order tunes did help out a little but a dyno tune at the shop would yeild more power but oh well...
The good thing is now that I have the tuner I can basically go to the shop and I wont have to buy a tuner from him and I can just have him program the car then upload his tunes on the SCT.
Whatever you do wont hurt, I would do whatever you can afford right now... In the long run going to the shop and having the guy tune your car and you buy a programmer from him would be the best way but if you dont have the cash laying around and want to fix it soon get the tuner from American Muscle, heres the link to it.
Good luck and welcome again!
SCT SF3/X3 Power Flash Tuner w/ 3 Free Custom Tunes (99-04 GT) at AmericanMuscle.com - Free Shipping!