Hi Paula
As you have posted a question here I guess you have access to the internet in order to research buying a computer.
So with that in mind have a look here:
http://www.ukorbit.com/computer_advice.htm
for some basic advice. I'm not sure what you mean by a "walkthrough" type game., but todays modern games take a lot of proccessing power to run and will cost more money. I would suggest that you pick up a copy of Computer Shopper at W H Smith, in each issue they have a section on buying a pc as well as lots of articles and adverts.
Expect any new PC to have Windows XP (the operating system) any applications software such as word processing, spreadsheets etc is likely to be extra.
As you intend to use the internet anti- virus software is essential but may only be included in a new pc as a trial version so you should factor this into your budget.
Hope this gets you started but many others will offer their suggestions. The important thing is to get as much advice as possible from friends and resources such as answerbank (it is free and people are always willing to provide it)
Good luck and welcome to the world of computing
Chris