Here are some options:
If you must have the Honda motor, the only sub $250 new honda powered motor is this
Troy-bilt. This is the same deck as on just about every MTD non propelled product over $150. It is plastic at the front and rear.
There are two models powered by the Kohler XT-6 to look at.
One is the Lawnboy 10603. Lawnboy is made by Toro. This is probably the best built deck of any the choices. It is a little heavy for its size and some have criticized it for its maneuverability.
The other is the
Husqvarna 6021p, which is what I purchased. Unlike the MTD products, the deck is all steel. It is constantly on sale at Sears online so you can get it for $185 frequently. The rear wheels have ball bearings. It is one of the easiest to maneuver push mowers out there. You can see some of my preliminary observations in the thread I started. Its recommended by Consumer Reports and they claim it is one of the best at mulching in the non self-propelled category, not that CR is the be all and end all of lawn mower reviews, but it is another piece to look at.
If you go with a Briggs motor, go with ones with the 625 or higher motor. If you do mulching, the smaller ones will not give you enough oomph. The advantage of the Briggs motors are that they are everywhere. Parts are cheap, plentiful, and they are easy to work on. Pretty much all your options with this motor in the price range you want are various brands of the same MTD mower. They run at about $200 and are at every major retailer in one form or another (troy-bilt, mtd, craftsman, yardman, etc). If you see the black plastic at the front, that is the same product as everywhere else and it is made by MTD. Sears does have an upgraded Craftsman version that includes a deck wash port and the 700 series B&S for $230. Sears again has constant sales online. The
$200 version frequently runs at $185 and the
$230 version goes for $215 when you add them to the cart. Other than the upgraded Sears version, these MTD mowers are all the same so just make sure you buy the version with a 625 or higher engine and buy it wherever you can get best deal or wherever has the best return policy/customer service.
However, before you lbuy a new mower, make sure to thoroughly check the used market. You may be able to find a better quality mower used under your budget.