Newbie here and so many questions

1. Masters swimming (www.usms.org) is a great place to start for swim help.
2. You'll be fine racing on your off-road bike until you determine how deep you want to get into this. You may want to make some minor modifications, like replacing knobby tires with road-friendly slicks.
3. Most people race in tri-specific shorts and tops, which are made to swim, bike and run in. The shorts  have a thinner, less absorbent pad for cycling so that you don't feel like you're running/swimming with a loaded diaper.

Welcome to BT, come here often to read the ongoing and archived threads and you'll quickly be one of the most knowledgeable triathletes-in-training out there.

Welcome!  I'm a semi-newbie myself, but I can try to answer your questions.

Swimming:  Check to see if your area has a local US Masters adult swim club.  They will have coaches that can work with you.  I'll let a female answer your training swim suit question.

Biking:  Being your first one, you might want to look at the idea of putting road type tires onto your existing mountain bike.  Your local bike store (LBS) should be able to help you with this.  This would save you a lot of money, and give you something to complete your first event with.  If you decide you like it, you can look into a more road specific bike.

Changing:  Most people wear a tri-specific suit that can be worn on the swim and then also on the bike and run.  You will have to put socks and shoes on, and that can be tricky when wet.  Tri suits are designed to dry pretty quickly.  If it is an open water swim (cold water) you might want/need a wet suit.  Tri suits are designed to wear under the wetsuit though, so when your cold water swim is done, you just peel off the wetsuit and go.

Re: socks. For a sprint or an Olympic distance, you don't really NEED socks. Train sockless enough to make sure you don't get blisters, stick some baby powder in your shoes and you should be good to go.

That being said, if you don't have clipless pedals on your bike, and are just going to wear sneakers for the bike and run, I suppose you could put on socks after the swim.

I am a newbie too! Welcome!

Swimming: I hired a swim coach instead of masters classes. It helped so much! My gym offers swimming lessons for adults. I chose the lessons because my form and balance needs work. A master class as I have experienced writes workouts on a board and then people swim the workout. The one-on-one was well worth the money spent.

Bike: You will go faster on a road bike but off road bike is fine. You may want to wait until you are sure this is what you want to do before making a big investment on a bike.

Changing: For my sprint I wore tri shorts and a tri shirt for the swim. At T1 I put on socks and shoes and got on my bike. The run I wore the same. Just make sure you practice in whatever you are going to race in to make sure it will be comfortable in all the conditions.

For my very first tri race it was a pool swim and I just swam in my normal bathing suit (which was a speedo type not a beach type so holds the boobs in nicely as I am not big in that area)  got out, put some leggings, T shirt over the top, socks and trainers on and wore that for the rest of the race (I still put socks on even now as I get blisters otherwise).

I had a very old bike which I put some new tyres on and trained on.  Your off road bike will be fine.  Don't spend money until you know you're going to like it and do some more. 

The only vital thing I would suggest to anyone is decent running shoes, but as you are a  runner you should have that covered already.

Oh and my other suggestion - start with a sprint one - and enter it - so you have an incentive to train.

Good luck and have fun 

Welcome! Welcome! Welcome!!!

I hired a swim coach for a month just to improve my form & it was a great investment.  Other than that, I've got a bunch of people here who continually support me with motivation, humor & are able to answer questions.  

I find BT to be a wonderful site & well worth the membership for so many reasons.  

Just muddle your way through for a little while until you figure out how you want to do things.  Have fun doing the research & playing around with the sport.

And, again...WELCOME!!

Welcome to BT and the tri-lifestyle. 

Do you have a swimsuit?  Is it comfortable enough to swim in? 
Do you have a bike helmet?  That's probably the only thing you might not already have.

I did my first triathlon (a sprint tri) with stuff I already had (swim trunks, mountain bike, running shoes).  Was I the only person on a mountain bike?  No, there were a few others, as well as a few people on vintage bikes.  Just make sure the bike is in good working order. 

Check with the YMCA, park district, or local college for swim lessons.  Group lessons to start are relatively inexpensive and will help quite a bit.  I've never swam Master's swimming, so I can't vouch for that although a lot of BT'ers do.  I've heard good things about Total Immersion and one of our local triathletes is arranging a TI clinic this winter. 

You might try riding the bike in your swimsuit (pull on shorts and a t-shirt over your suit if you want) to make sure it doesn't bind or rub in the wrong spots while riding, and try running in it (you may not like the amount of support a swimsuit provides for running).  If it works for you, then wear the swimsuit for that first race.  You won't generally have a place to change between the swim and bike (or bike and run), but I have seen people do some creative things with an XXXL t-shirt and/or beach towel.  One thing to try before the race is putting clothes (socks and t-shirt especially) on while you're wet (and usually breathing very hard) after the swim. 

Keep in mind, most of us aren't going to win the race, or even place in our age group, so an extra 30 seconds adjusting your socks before you start the run may be a great time-investment. 

I was in your same position in the summer of 2006. I had the same thoughts about buying a cheap bike. Now it is 2008 and I bought my 3rd bike this summer.

If you like competition, and you like to push yourself, you will probably love tris. Just sayin'.