The 60D, 70D, and 80D are not at all in the same category as the EOS Rebels.
Internationally, the Rebels are known by a three digit number and a D in Europe and Kiss X# in Japan (450D/Rebel XSi/Kiss X3, 500D/Rebel T1i/Kiss X3, 550D/Rebel T2i/Kiss X4, etc), but they are the same. The Rebels are the entry level cameras from Canon (and they even recently started a more entry level with the same T#, but no i: T5i and T5 are not the same. I have had a T1i since May 2010, and it's still a very capable camera that I use for backup and second. It's video system sucks, though.
The next step up is the advanced amateur cameras. This is the ##Ds, like the 60D, 70D, and 80D. These cameras have a bigger body, more features (like two wheels instead of one, better screens, better processors, brighter pentaprisms instead of pentamirrors, etc.) Like Hoag said, in general, high numbers (with the same number of digits) are more advanced, except in the cast of the 77D, which occupies a weird position between a Rebel and a 70D. It has a newer processor than either the 70D or the 80D, but it has the slower max shutter speed and flash sync of a Rebel (1/4000 and 1/200 vs. 1/8000 and 1/250, respectively), and has a rebels mirror box and view finder design. I bought a 70D in 2014 to take two bodies with me to the Galapagos and it is now my main camera. Starting with the 70D, the camera is able to retain autofocus in video and live view modes through Dual Pixel AF, which was a huge step for DSLRs.
Stepping up further is the 7D, 6D, and 5D range. These are all very different cameras, but could be put into different, but similar levels in the ranking. The 7D is aimed at the advanced amateur/prosumer birder or sport photographer. It is still a 1.6x crop sensor, but has a pro build, including improved weather resistance (the Rebels have none, the 70D and 80D have some, but Canon won't give details). The original 7D is getting pretty long in the tooth, so I wouldn't recommend it unless you can get it really cheap. Anything you find used will likely have had 50-100,000 shutter actuations by this point. The 7D II has dual card slots and can do either CF or SD cards, and you can record to both at the same time so you have a back up in the event of a card failure. It also has dual processors and can machine gun 10 frames per second with full AF in between (which probably isn't that important for shooting still cars, but would be nice at the track). The 6D II is the current "entry level" full frame offering from Canon. It lacks a lot of the features your going to find in a 5D, including a Rebel-like max shutter speed of 1/4000s, lower max ISO, fewer AF points, SD cards and no support for CF cards, and a 98% viewfinder coverage (equivalent to the 70D). The 5D is the top of the advanced prosumer, with three different current models: 5D IV, 5Ds, and 5Ds R, the 5D IV being the newest. The 5Ds cameras are Canon's venture into the ridiculous megapixel wars, at 50.6 megapixels. The 5D IV was Canon's first 4k capable DSLR. In this category, only the 7D has a built-in flash, so you'll have to add on another $300 minimum if you want a flash on the others (of course, you have to do that on any camera if you want a decent flash because pop-ups suck). A lot of pros I know use the 5D III or 5D IV.
At the very top of the top is the 1D X series, which is Canon's ultimate flag ship. The original 1D was a weird not quite APS-C crop called APS-H, but since the 1D S, they have all been full frame. These cameras are given the ultimate in weather sealing, usable in a driving rain with an L series lens. This is what the guys in the endzone are shooting with those big white lenses when it's pouring. The 1D II can shoot up to 16 frames per second and 4k video. It is the only series that doesn't have an optional battery grip because one is built in to the camera from the beginning. No mortal human actually owns one of these because they cost $5,500.
One important thing to remember, if you are coming from a 450D with lenses: EF-S lenses are only compatible with APS-C cameras (7D, ##D, and ###D/Rebel/Kiss). They physically will not fit on a 1D, 5D, or 6D, and will cause damage to the mirror if you try to use them. Nikon has an advantage here in that they designed their cameras to work with all of their lenses, but you just get a really small image circle if you use a crop sensor lens on a full frame camera. All EF lenses will work on all Canon DSLRs.
Hoag makes a good point about waiting to get the camera until you can get the housing at the same time if you want to go that route. Housings to match your camera will be discontinued at some point, but if you get a current model camera, you'll probably have about a five year window. Lens ports and accessories tend to work with a wide range of housings (the housings have to be specific to the button layout and form factor of the camera), so you could buy it in pieces.
I still happily shoot with an old S110 P&S in a housing with a Sea&Sea YS-03 flash underwater. It's bulky enough that I don't have much interest in bringing either of my DSLRs with me. The S110's popup flash triggers the YS-03 through a fiber optic cable, and the addition of an off camera flash made a huge difference in what I can get from that camera.
