Bike advice??

Welcome both of you to the sport. 

There are a couple very basic requirements for riding a bike in a triathlon. 

First:  Helmets will be required and are generally required for ANY riding at the venue even before or after the race.  Yup, you can get DQ'd after the race if you ride your bike back to your car without the helmet in place. 

Second:  Bikes are required to have two wheels one behind the other, functional brakes, and in mechanical order that they aren't a threat to other riders (so, handlebars must be plugged, nothing loose that can come off). 

After that...you'll see all types of bikes at many races.  I did my first two races on a steel-framed mountain bike and had a blast.  I saw a guy riding a mountain bike during a half-ironman (56 miles on the bike). If you've got bikes and they meet the above criteria, RIDE THEM! 

A triathlon bike has slightly different geometry that is more optimized for the sport and non-draft riding.  They'll usually have slightly upturned outer bars (often called bull bars, they look like horns on a bull) and aero bars with forearm rests.  Road bikes have the curled-down handlebars.  You *can* add aerobars to a road bike (or a hybrid) and they're usually called "clip on" bars.  Riding in the aero position is usually good for ~1 mph improvement over riding "on the hoods" on a road bike.  But...it's hard to climb hills in an aero position and it takes a lot of riding to be comfortable in an aero position.  The geometry helps with running after riding, but unless you're riding 22-23 mph and running 6-minute miles, that's a big price to pay for a very small gain. 

For either, bike fit is important.  There are some online calculators that should get you a rough idea of what size bike to get.  This is also a consideration for buying a bike at a local bike shop (LBS).  They'll try to get you fit on the right size bike and do a basic fit, plus buying from a LBS usually gets you a bike tune-up after you've ridden it a month or two. 

Here's a mantra:  There's no such thing as a "cheap bike."  That used Schwinn that you pick up for $50 at the garage sale...New tires and tubes are probably $35+ per wheel.  Brake pads another $10.  A chain anywhere from $10-50.  If you're paying the bike shop to do all of this work, you can expect to spend $200 or so on a basic tune up and inspection.  This doesn't include replacing cables or trueing a wobbly wheel.  If you are mechanically inclined, you can do some of this yourself, but...without experience it's hard to get it right. 

Now, after you've got a bike, you'll want a tire repair kit (and probably a small bag to store it in), water bottle holders, pump or inflator, spare tubes, etc. 

Clipless pedals and bike shoes will be another *eventual* purchase. 

You didn't ask, but...riding a road/tri bike is the most efficient riding (you'll go faster for the same energy or use less energy to go some speed/distance) because you're on a light weight frame with skinny, high pressure (100 psi) tires and "hunched over" for the lowest wind resistance.  But...there are a few drawbacks.  The riding position isn't comfortable starting out and may not be a great choice for busy roads.  Those skinny tires tires are easily damaged by glass, wires, sharp rocks or hitting bumps really hard.  They also aren't great if there's sand or gravel on the road and can slip into the slots of storm drains.  You may enjoy riding your hybrid bike a lot more even if it isn't as fast or efficient. 

Road bikes and tribikes are both good options for triathlons.  A road bike has a different set up for the handle bars.  They have the curled drops with the breaks on them.  Triathlon bikes have are rests and aero bars.  The aero bars make you thinner which means you have less drag and go faster for the same power output.  You however don't have the breaks where your hands are so reaction time to break is half second slower.  So, you don't ride in close packs on an tribike like you can with a road bike.  Also some people can not produce as much power on an aero bike as they can with a road bike just because they are not as upright and open.  So some people can go faster on a road bike but they may not has legs that are fresh off the bike because they are producing more power.  If you are going to do a lot of group rides and mixed cycling events then a road bike is what you may want.  If you are just going to do triathlons then the tribike may be the better option.  I personally only have a tribike.  My cycling is pretty much exclusively triathlon training and events.  I have done group rides with they local triclubs and did the MS150 bike ride all on the tribike and it was fine.  I wasn't competitive in triathlons for  first 3-4 years so the bike I was on didn't too much.  I mountain bike would have been a bad idead because it would have turned my 3-1/2 hour bike rides into 4-1/2 hour bike rides and that might have killed me, but at races I was just trying to beat my own time from previous races and was not worried about beating anyone else out on the course so I just let the guys with $10,000 bikes speed past me and was more the pacing plan I had and how I was executing it on my $300 aluminum frame Tribike. I did upgrade to used bike that were $1500 and $1650 later on.  One of them was a top of the line race bike that the previous owner hated because it was a poor fit to him.  Get a bike that is fun to ride.  If it is fun to ride then it is probably a good fit and you will probably make a lot of progress on it which is the what you want.