As I said, finding the right seat isn't the easiest thing in the world (well, it is if you're not picky).
If you look at the spec sheet drawings, for example, the Drake's seat holes to the front of the bowl is about 18.5". So you go down to HD or Lowe's and look at the packaging and find one that lists it as being 18.5" from hole centre to seat front edge. You take it home, install it and then find that it over hangs the toilet seat by 0.5". (It happened to me.) Now you have to take it back to the store and exchange it for another, and another, and another, until you find one you like.
Finding the height is easy, just take a small ruler with you and measure from underneath one of the two front foot pads to the top of the seat (not the cover, obviously). You might find one or two at 0.5", many at 0.75" (plastic) and 1.0" (plastic and wood), and some at 1.25" and 1.5" (typically heavy wood). Some people like the squishy rubber/foam seats...
With my ADA Drake I settled on a Kohler seat (Kohler Bravia Q2 Advantage, part number 4774) because while it is easy to remove the seat for cleaning, it's big advantage is that the mounting hole "pad" can be installed two ways, one giving a slightly shorter seat (closer to 18,5") than the other. With both the Kohler and the Toto seat I have about 1/16" of an inch overhang. With others I had 1/4" and 1/2". The Kohler packaging and website says that it is 18+5/8" (18.625") on hole centers. So the overhang should be about 1/8".
What looks like a thin seat:
http://www.us.kohler.com/webassets/kpna/catalog/pdf/en/K-4761-CP_spec.pdf
http://www.us.kohler.com/us/Avantis-Quiet-Close™-elongated-toilet-seat-with-Quick-Release™-Polished-Chrome-metal-hinges/productDetail/Quick-Release-Toilet-Seats/426118.htm?brandId=972299&skuId=398815&categoryId=972298&hash=id=filters&startIndex=20&scrollTop=0
13/16" - or between 1/2" and 3/4". For the money it may be better to go with some $30 seat instead.
A thin seat:
http://www.bathstore.com/products/universal-ultra-thin-soft-close-wc-seat-2430.html Good luck trying to find it in the States, though.
Kohler & American Standard ADA toilets are 16.5" high. At least Toto is a little better.
Some manufacturers have spec sheets for their seats, most do not. They are not the easiest things to find, even on the Internet, much less on the store packaging. Then you'll need a T-square and a ruler. You will probably get some strange looks from the store clerks as you try and measure the seats, if they will even allow it. Besides the length look at the width, other wise you may get overhang on the sides.
To me, the perfect height is 15.5" - 15.75". ymmv. It's not something we really think about. Until you get bad knees and have to use a short toilet. One difference is that at work we are wearing shoes, so it being 1/2" too tall (ADA) typically isn't a problem. Being 1/2" taller (wearing shoes) while using a standard height toilet with a slim seat can be a problem, though. But chances are that the seat at work is about 1.0" if made out of wood and 0.75" if made out of plastic. But when one is at home one may not be using shoes or sandals, so the height is taller when using the ADA toilet. Then you will need a thick small carpet in the front, one that you will probably need to replace often if males use the toilet standing up. If you have an ADA height then the wife will need to always wear thick sandals when using the Loo, which could be an inconvenience if she is just getting out of the shower.
The shape of the seat can be disconcerting to some, like the Toto seats that make it feel like you're falling in since they have deep dish edges. Some get flimsy foot pads on their seats and when they break (typically on wood seats) they need to get new seats. Or wooden seats crack. Or the seat slides or slips side to side. That is usually a mounting hole problem, but you may need to put a little traction grip tape on the foot pads to help even more. So when you find the perfect seat you may want to buy two, one for the future when the seat needs replacing.
A lot of guys seem to like a certain American Standard seat. It has the same size as the Toto toilet - 18.5" hole centers and 14.0" wide. Every time I looked for them at HD they were out so I don't even know what they look like.
You have two other "kickers": if you have children you probably won't want a heavy wood seat that can smash their fingers, so it's light plastic or slow close. For children you may want a smaller inside hole. Then there is colour selection - the wife may want an exact match with the bowl colour. If you can't match it exactly then you may need to match it with the bathroom curtain or the vanity colour or the rug or the bath towels - whatever will make her satisfied.