All depends on your bank account 聳 and your aspirations. That’s because any ol’ bicycle will get you around the typical tri course, which tends to be rolling-to-flat, rarely with big climbs. But if you want to start finishing with the leaders, then of course you聮ll need a more exotic machine. The only “must” I’d offer is this: “Thou must have a road bike.” True, first statement in this answer indicates that anything with two wheels will suffice. But I’m assuming you want to at least look like you’ve done this before. That, and the weight and non-aerodynamic qualities of the average mountain bike, mean that such a cycle is a poor choice.
The OCR3 from Giant
So, what kinda road bike? For a basic pair of wheels, it’s very difficult to beat the Giant OCR3 (www.giant.com). For $600 you get a light, snappy aluminum frame, good-shifting Shimano drive train, and good-quality Michelin tires. It’s just a tremendous buy in a pretty serious road tool. The only drawback is that it’s sized small/medium/large, so if you’re a between-sizes guy, you might have to make some compromises there. For a step up, the KHS Flite 500 ($1,000) gives you a better-quality parts group with a very stiff frame (better power transmission) and race-ready tires. But its frame may be too stiff if you ride rough roads often. And if you want to spend serious dough, Trek’s 5200 is not all that dissimilar from the bike Lance rides, for a lot less money — $2,800.
You will find that there also are such things as “tri” bikes, which usually have aerodynamic tubing and handlebars set up for long periods crouched over aero bars. A good example: Cervélo聮s Dual Ultegra ($1,600). But they’re not “all purpose” bikes, so if you want to ride and race all-around, stick with a true road bike.