If your plan is to mow a 1/4 acre of land, and the other acre for garden? toys? house and house accessories? or like on mine, boats, car projects, etc?
A poorly built mower deck such as a common cheap rider these days could cost a couple hundred dollars every couple of years to maintain/rebuild.
A 1/4 acre is almost too small to use a rider on efficiently, but if you did a rider a small mower deck I think would be preferred so as to have better control of your cut when in so many turns and small areas.
I think the most efficient way to mow 1/4 acre might be a push mower and one that usually gets overlooked but is very cheap under many different names such as Bolens or yard machines, etc, but is MTD, I think. I n the picture you see the Husqvarna all wheel drive self propelled overpriced $350 push mower and the Lowes special $125 Bolens push mower.
The Husqvarna works very well, no complaints except this, it is so heavy that something so simple has been made so hard for very little benefit. The Bolens on the other hand is so light that it is very little effort and with the Northern Tool rear cart wheels (with ball bearings) it will roll on its own when you give it a push and let go. Sure it is loud, and vibrates and the paint was me and my son. I know its not sexy but you can always add fancy letters if it needs it.
The Husqvarna might outlast that Bolens because no one in my family wants to use it since the little Bolens is so light and easy even though It was the point of some jokes by my two boys at first (one in college and one almost there, they think they know everything, just ask them
). By the way, the Bolens just won't quit, I think the mower deck will fail before the cheap Briggs, but it works.
So my logic is this, mower decks on riders are a pain to keep running with extra expense for very little possible benefit (1/4 acre), unless you pony up for a deck that has cast iron, quality bearings, proper engineering to last, and the machine attached to it will also be very spendy, quality costs (I've learned this lesson with my GT). If a Bolens costs you $125 every two years (because you throw it away and buy another) then you have very little maintenance (personal time) and the grass gets cut. A good GT may be easier to find if you aren't strapped to get a mower
deck, or a deck that needs a lot of work.
A GT such as some of these that have been mentioned would be very useful, I too, through experience, have become a believer in the older steel. Many of these machines would be indispensable in all the uses around the yard to include toy round up time with a large yard trailer and such.