Advice needed from veterans for a first-timer

Welcome!

With your running background you have the overall fitness already.  I've run marathons, and I've done many Olympic distance triathlons.  Triathlons are easier to train for, and the recovery after an Olympic distance tri is much faster then a marathon.  I've raced Olympic triathlons on back to back weekends.  The weekend after a marathon, I'd be lucky if I was running 5 miles at an easy pace.

As far as swimming goes, I'd encourage you to work with a coach, or sign up for a swim workshop such as Total Immersion.  Swimming is a very technique driven sport, having someone work with you on your form will help you be more efficient in the water.  Don't worry about speed.  Work on form and endurance.

Runing does help the biking somewhat, but you're using different leg muscles so it doesn't all transfer over from the one sport to the other.  Someone did mention bike fit already, but I will repeat it.  Being comfortable on the bike is VERY important.  If you're not comfortable you will not be efficient on the bike.  If you're not efficient on the bike, you will have not have much left for the run.

The challenge of triathlon comes from putting the 3 sports together in such a way that one doesn't wipe you out for the next.  Having a smooth stroke, and being efficient in the water is going to give you more energy for the bike ride.  If you have more energy for the bike, and are comfortable on the bike, that's going to leave you in better shape for the run.  Being that you come from a running background, you will go into that last leg with your "strong" event left.

After you've gotten some more mileage in your bike legs make sure you do some "bricks". This is where you do a ride, and immediately switch shoes, and go into a run.  You'll be surprsied the first time you do it, how dead your legs feel when you first start running.  Those first bricks don't have to be all that long. 10- 15 mile bike, and a 2 mile run.  Later on you can go for a longer brick, but it's not even absolutely necessary to do the full distance in a brick.

Use this site to its fullest.  There are a lot of very good articles and training plans.  Also continue to pick the brains of your fellow BT'ers.  I'm a hard core veteran who can offer a lot of advice from my 20 plus years in the sport, but the guy or gal who did their first triathlon last season, or even last month can also give you a very fresh look, on what it's like to prepare for that first race.  The relative newbie is going to remember a lot more about prepping for his/her first race then I'm going to remember about my first race in 1983. 

I will admit, I still have my training and racing journals from 22 years ago,  and some of the entries in these journals are pretty funny, and an interesting take on how the sport has changed in 22 years.