What kind of Lawnmower are you looking to get?
There are a lot of different kinds of lawnmower including push mowers, self propelled mowers, riding mowers or robotic mowers. A push mower is recommended if your garden is evenly sloped whereas a self propelled mower is recommended if your garden features hills and slopes. A riding lawn mower is recommended if the amount you intend to mow is over 1/2 an acre. the robotic mower is a fun choice for smaller lawns.
Choose what kind of power
This mostly concerns push mowers whether you would prefer an electric or gas mower. Electric mowers have the advantage of conserving energy and money whereas gas mowers have a bit more kick to them.
Some things do not affect lawn quality
Horsepower and engine size etc. do not have an effect on the lawns quality so while it may be tempting to buy that big engine with its something ridiculous small car horsepower its not necessary and will not affect lawn quality.
Choose a brand
While this in itself does not affect the lawnmower it does change where and how easily you can get it serviced or repaired if need be.
Set a price range
Some lawnmowers can be very expensive and its better to set your price range first then look to make sure you don't overspend on it.