As this is your first tri Just go and enjoy. TIME IS NOT IMPORTANT.
Once you have finished and decide like the rest of us that tri's are the way to go then you can worry about time. As you get fitter and more experianced your times will drop and then you can worry about them.

That's a really subjective question that depends on a lot of factors: your gender, age group, and experience, which you didn't provide in your profile. One place to start is to see how others in your age group did at this distance in this race. Another idea is to determine how fast you could do each one individually and see how close you could come to those times in a combined race.

But to give you some real numbers, since you asked, what I would shoot for:
Swim 800m in 14:00, or 1:45 per/100
Bike 20 mi in 1hr or less especially it is is as flat as I remember Louisiana to be
Run 3.1 mi in sub :20

And if I hit those number I am sure I would be middle of the pack in my 35-39 M age group :(

FYI - There are Olympic-type distance coming up in your area:
1. TriAmerica in New Orleans (sorta) on May 24, 25
http://www.triamerica.com/

2. Louisiana Red River Triathlon in Shreveport, June 1

3. How about River Cities Triathlon (Olympic) in Shreveport in August?

A sub-20 3.1 mile run is considered middle of the pack for a 35-39M age-grouper??? I think that would be one of the faster times from what I've seen.

As others have stated, just enjoy it. It's your first race, don't get hung up on the numbers and just soak up the experience.

Rivercities has the BEST giveaways ever. I think last year for my $80 entry, i got $100 worth of stuff. (2 shirts, a hat, a tri bag, sunglasses, socks, and some other stuff)

The bike is rolling, but fast, and the run is humid.

Lots of people say to just go out and enjoy the race without thinking about time, and they are right. My first triathlon (olympic) I did was a 2:22/100 swim, 16.8MPH bike, and 8:36/mi run. No regrets at all. I finished and had fun. 3 weeks later later I was in the same triathlon (sprint) as my brother, and I wanted to beat him. My times dropped to 1:51/100, 18.1MPH, and 7:30min/mi.

There will be lots of triathlons to set and achive time goals. You can only have one first triathlon. I see no problem with setting the bar nice and low so that your 2nd race is a PR also. :)

I think going "easy" and enjoying your first tri is good advice if you haven't been a competitive endurance athlete before. But for the many people that come to triathlons from racing track or swimming, its hard to enjoy the experience if you aren't racing for a goal time of some sort. That was true for me at least, and some others I know that were in a similar situation. I spent my first summer of training figuring out what kind of paces I good sustain for each leg, and then I set a clear time goal and set out to beat it. I spent a lot of time studying results from the previous years trying to figure out where I would fit in on each leg, and where I could place overall.

My goal was 50th place, and to get about 1:20. I finished in 46th place with a 1:20:24. I was racing hard the whole way and very concerned about my time and place, but I enjoyed the entire experience very much.

I agree with Sully and had a similar philosophy for my first tri. I came from a mountain biking and running background, so had certain performance expectations for those legs. I would take your stand alone times for each leg and add a little time to each,since you will be doing them in succession, then add a couple minutes for transitions for your goal time.