ATI Radeon is a product line, not a specific model. You will have to provide us the #. Generally, more video card ram is needed as the size of your monitor increases--so I would definitely go with 512mb if you want to use dual monitors.
I assume its most likely a Radeon 4350--which is a decent card if you plan to only surf the internet and watch videos. Its not really good enough for computer gaming. So that you are aware, this card is worth about $25-30 if bought on the internet, but major vendors such as dell usually charge about $60 for the card. If you want to be adventurous you could probably save a few dollars by sticking the card in yourself.
If you would like to post more details we could help you with the entire purchase.