Looking for advice on a buying a new bike

If you're relatively new to cycling and triathlon, then probably your best bet is a mid-range road bike (probably toward the low end of the price range you mentioned).  You can certainly get an aluminum frame with some carbon bits, and maybe a full carbon frame if you shop around.  Look for components equivalent to Shimano 105 or Ultegra, especially for shifters & rear derailleur

It can be tempting to go for a bargain basement bike so you don't put too much money at risk.  This is a bad idea, since you won't really get the experience of riding a decent bike, and could get put off the sport entirely just by having bad equipment.  Alternatively, you'll very quickly want to spend a bunch on upgrades or a new, better bike.

I think you also want to avoid spending too much and going too high end.  If you're new to cycling, you don't really know yet what your preferences are, what you like and don't like, what fits you and what doesn't over the long run.  You don't want to be stuck with a blinged-out super bike that is a great ride for somebody, but not for you.

Get something good that you can ride, race and do minor upgrades to for a couple of years, and then think about the perfect bike later on when you've got more experience and knowledge.

If you watched the Tour de France, tri bikes are similar to the bikes they ride for the time trial stages, as opposed to road bikes for the other stages.

Most visible difference is that a tri bike has "bullhorn" handlebars and aero bars, and are designed to be ridden primarily in the aero position.  Tri bike frame tubes also usually have more aerodynamic shape, and the bike has a steeper geometry (seat tube closer to vertical) than a road bike.

Road bikes are ususally more versatile and more comfortable for general riding (some folks will disagree, but I did say "usually"), and you can add "clip-on" aero bars to the drop handlebars on a road bike and do other adjustments to make them more efficient in aero position.