Electric models are available, just as they are in standard push mowers. The batteries are sturdy and you can generally get a 1/2 acre or more mowed before recharging is required. They're quiet and don't produce any fumes. But they don't have the power of gasoline-powered tractor mowers and can get stuck in thick brushy areas.
Some models have reel blades that shoot cuttings out the front, but those are usually designed for professional lawn care specialists. If you don't have a golf link to mow, the rotary type is for you. The mowing blades are usually below the deck on which the seat resides, which does produce a bit of vibration. But a good soft seat will minimize that to well below an acceptable level.
The smaller types are often called 'riding mowers', but the design is essentially the same. The difference is often just in physical size and horsepower of the engine. More horsepower is usually better, but efficiency comes into play. If you have a well built model, it doesn't require as much horsepower to do the job.
Also, if you have a very smooth, level yard less horsepower is required. Conversely, if your area is hilly with several slopes, more may be required to maintain those. For that, the lawn tractor is the preferred choice.
The engines are in the 10-15 horsepower range which is still considerably less than the 150-300 horsepower range of the typical car engine. In general, you pay more money for those with more horsepower. Be sure you need it before laying out the extra cash.
Prices tend to be higher also for those with wider cutting areas. Lawn tractor blades can range between 38-42 inches (96-107 cm). The wider blade will usually cut more lawn quicker, getting the job done sooner. But keep in mind that the difference is only about 10% and the inaccuracy with which you steer it may more than make up for the difference.
Of course, it's possible to get a garden tractor, with 20 horsepower or more and up to 60 inch mowing blades. Few will need that, but the extra power can be handy if you use it to haul dirt, brush or tree parts around in an attachable trailer. Here again, you'll pay more to get more.
Check out the turning radius on the model you're considering. You may pay more for a very tight, or even zero, radius model, but unless you have areas that are very difficult to navigate the feature probably isn't worth the extra cost.
Sit on a unit, get a feel for the steering mechanism and controls. Ensure that they're within comfortable reach and made from sturdy materials. Lawn tractor or rider mowers can easily cost from a few hundred to a couple of thousand. So, you'll want one that makes the job easy and pleasant, while being reliable for years to come.
Sooner or later, anyone who has to mow the lawn every week or two for several months will begin to long for a ridable mower. These small tractor-style units are a true blessing for anyone with a 1/4 acre or more to keep neat.