Yes, the cards you linked are what you need. Someone may disagree with me here, but really any 'g' card will do the job for surfing the net, sending emails etc. You don't need anything fancy. (I have a number floating around which I use in my work laptop. Old, new, expensive and cheap. There's no difference between them. In fact one of the cheaper ones gives me the best range in the garden.) The one at the top of the page will do the job just fine. The laptop is new enough to be able to use any card you buy, ie, it's beyond the backward comapatability point mentioned by Tinstaafl.
You will need this card as I checked the specs and an Inspiron 1200 does not have built in wireless capability unless it was specified as an extra, which is most unlikely and may not even have been an option.
Option 1. Yes, entirely correct.
Option 2. Yes, entirely correct.
Which option you take is entirely a matter of cost over convenience. I'd plumb for the latter though for the sake of about an extra £30 or so. It's likely to be easier to setup and less 'glitchy' in use.