$2000 max leaves you few options. I would go used and over shoot your grade, but if you are determined to buy new you have few options.
John Deere - buy green pay green in this category. You get the deere name and most of the time a deere dealer that will refuse to work on it. Your transzxle will be the first thing to go in this class.
Deere uses a Tuff Torq K40 and a Private Label Kawasaki engine now.
Husqvarna, Sears, Bolens, Ariens, weed eater- These are all the same tractor with different engines and body work. All built in the armpit of South Carolina. Worst plant in their entire global network build all of these tractors. Ariens at $1250 with a 42" deck is the same as a Sears with a 42" deck. Different body work but the working bits are the same.
MTD, Toro, Cub Cadet - Toro is the outlier here. They only let MTD build a certain price point for them and this is it. Otherwise, you are back to the Getting into a little better class of mower, you are also bumping the top of your budget. Larger Toros are built by Toro, but again out of your price point.
Simplicity and Snapper, both owned and manufactured by Briggs and Straton and both are very good products. Just watch which one you get for the environment you are using. Both of these are moving up your price point these days, personally I think they are a good value.
The trick in this price point is the gear and tires. Most of the hydrostatic units have a K40/K46 Tuff Torq transmission in them or a T2 Hydrogear. The T2 is a stronger transmission, but we are looking at marginal differences. There is no difference between a K40/K46 transaxle.
Get the smallest tire possible and you will do fine. Switch the transaxle fluid over to Rotella T synthetic. In our testing we have found that is the best fluid for this class of transaxle. We bench mark everything else against this.
That being said I would get the Ariens, check to make sure it is assembled properly (99% of their warranty issues are assembly problems, horrible factory), and switch the engine and the transaxle over to full synthetic and be very happy with your purchase.
Remember, smallest tire, verify proper assembly, switch to all synthetic and enjoy.
SOURCE: Engineer for Tuff Torq for 4 years.