You'll obviously be needing a decent printer too. If you're going to do business - you should be doing it right. Shop around and take a little time to get familiar with what's available in your neighborhood. You'd also be required to pay for the shipping one way - to the repair facility. With a locally purchased computer, when a serious problem arises your unit can be taken back to the store and generally fixed on that very same day.
Worst case is usually by the next day . . .
If at all possible try to purchase a computer that won't need any upgrades whatsoever for at least 3 years, and possibly even longer than that. However, the fact of the matter is simply that for any single user, home business, and even many small businesses, either of these processors will work just as fine as fine can be. Make sure that you have a 56K V90 based modem too. Don't get anything that you won't need - because that would be yet one more piece of hardware that you'd have to learn to operate. Software should consist of some type of Office Suite which combines Multifunction Word Processing abilities along with Database and Spreadsheet abilities.