Newbie Questions.

I'm not sure what you mean by the 'running tights' question.  Most people race in triathlon shorts (which are also designed for swimming and biking.  But in my opinion, this statement ('train like you plan to race') is overused.  You should in many ways NOT train as you race.  Your training should be mostly less intense than your race pace, for example.  But without more specific information about your athletic background, it would be hard for anybody to make specific recommendations.

Most, but by no means all, people use bikes that require special shoes.  Your local bike shop can help you out there.  If you use a bike that does not require special shoes, then sure, you can run and bike in the same shoes.

 

The sky is the limit here.  But I'm guessing from your questions that your best bet would be to beg borrow or steal an inexpensive bike, train on it, and try it out.  If you get hooked (which you will!), then look into buying a nicer bike.  For your first tri, anything will do, really -- a mountain bike, commuter, whatever.

But if you are bent on buying a bike, the sky's the limit on price.