In that price range I am partial to the Lenovo computers in this current generation (decent keyboard). Get something with at least 4GB of RAM. Obviously we can get into a lot of details but most full-size laptops will work well for what you want to do.
I would recommend going to the store and trying out a few computers. Nothing in that price range is going to be built like a Macbook Pro, but you want to look at a few things:
1. Keyboard. How does it feel?
2. Touchpad. How does it feel? Are you OK with the texture? Is it accurate enough for day to day use?
3. Screen hinge. Does it feel solid enough, or is it wobbly and flimsy?
If she doesn't get a MS Office license through her school then buy a "education" or "student & teacher" version which is greatly discounted and intended for people such as your wife.
On a computer that is under $400 I absolutely would not buy a performance plan. If there is something terribly wrong with the computer you will probably know before the warranty is out (usually 1 year). If something major breaks after that time, you can usually find parts cheap enough online. If it isn't something simple (screen, HD, keyboard, battery, power cord) then it probably isn't worth fixing.
Whatever Windows PC you buy, it will come with a bunch of "bloatware" installed. Removing that stuff ASAP will greatly improve the speed of the computer, and reduce your eventual headaches.
As a little bit of background, up until about a year ago, I worked as the main electronics purchaser for a chain of rent-to-own stores. It wasn't a large chain, but I usually purchased about $15,000 worth of computers each month. I was also involved in repairing the broken computers. Most of the computers I bought were in the $300-$700 range.
As far as long-term reliability goes, my experience in the rent-to-own business has shown me that with the low-end computers you don't quite know what you're getting. Generally, the Toshiba low-end computers seemed to require the most repairs, followed closely by Asus. I'm not saying that they are always the worse (I have an Asus that has been great, but it's not a low-end machine) but in general I saw the most broken parts on those machines. MSI were also bad but those aren't sold in most "big box" stores these days.
HP had a few generations that were good, then one generation where almost every single laptop had serious problems. The generation after that was good again; my point being that every manufacturer puts out some good & bad machines.
Dells were generally good, as were the Lenovos.
That said, I wouldn't hesitate to buy a low-end computer for the type of work that you're wife is planning to do with it. I'm typing this on a Dell Inspiron 1440 that my wife bought 2.5 years ago for $500. It is not a "top of the line" computer but it held up for her through 2 years of school and now a semester's worth of law school with me. I have replaced the keyboard ($18) and one battery ($35) so far. It is a little scratched up but everything is still tight and functioning well enough for me to use it 10+ hours a day, 6 days a week. I don't like the touchpad on this machine but I make it work.