Probably just about anything will work for your needs, HOWEVER, there is one consideration. Windows has a tendency to trip and fall (crash) if run on poor quality hardware, so this presents something of a conundrum for people like you.
On the one hand, you don't need anything fancy, so there's not a lot of point in spending a large amount of money on this. On the other hand, cheaper systems tend to have the lower quality hardware which makes Windows a real pain to use.
So, you'll probably just have to accept that this is an unavoidable risk, and the best you can hope to do is mitigate the damages so to speak.
To that end, I would personally recommend AVOIDING the following brands: HP, Compaq, Acer, Gateway, and eMachines. In my experience, these systems have a much higher problem rate compared to others. So that leaves Apple, Lenovo, Dell, and Toshiba as your primary choices. You can also include Sony if you like, but I tend to just ignore them because of some of their rather... disagreeable... support policies. Any deviation from the factory configuration is generally grounds for them refusing support.
Apple and Lenovo/IBM are probably a bit pricey for what you need, so the field is narrowed to Dell and Toshiba.
One other consideration, is the new category of netbooks. These are generally small, lightweight, laptops, sacrificing a lot of onboard computing power on the premise of using web based apps. They should be fine for some light MS Office use like typing letters, and that, but if you do a lot of complex formulas with your Excel book keeping, then that may rule these out. It also kind of depends on the games the grandkids want to play. They might well run acceptably on a netbook. If you tossed out a few example titles, someone might be able to give you some idea.
In any case, Windows does not come with any programs like Word and Excel, but if you don't want to buy a new copy you can check out OpenOffice or Google Apps. Google's online apps are pretty basic, but sometimes that's all you really need. OpenOffice is a bit more full featured, but will demand more resources of your system. Everything's a tradeoff with laptops/netbooks.
As for the specifics of the system itself. Just avoid anything that says the CPU is Celeron anything or Pentium anything. Core 2 Duo is good, as would Athlon64 or it might say AMD Phenom. All perfectly fine. Netbooks will almost universally have the Intel Atom, and there's no real choice on those at the moment.
Just look for the processor with the highest number that's within your budget, and the largest amount of RAM and hard drive space. Again, within your budget.
I have a home computer loaded with XP and use it for writing letters Microsoft Office Word, bookkeeping on Excel, posters for grandkids on Powerpoint, email, home shopping, solitare and facebook contacts with family. I have to get a laptop to take on a trip to a computerless home. I don't know what to get. I am not a technical person, I push buttons as I need them pushed. I am asking for simple to understand advice on what to get and if this new Windows 7 has the word processing/ecel/powerpoint I already know how to use. I also have a couple of games loaded for the grandkids to play. If you can type simply so I understand what to consider, I would be most grateful.