I'd be really cautious about adding items with a cost to a customer's shopping cart automatically. I for one would be miffed if I was ordering a $10 item and had an additional $1 item that I had to pay for but that I hadn't asked for...
Regardless, it's only a marginally hard thing to do.
Basically, you need to create all of the $1 products as regular $1 products but don't make them available on your site. (Or do, not sure how you wanted to handle that.)
Now you need to write the custom code for the $1 gifts. I would create a new page for this. I'd change the 'checkout' links to go to this new page.
On the new page I'd alert the customer that they had qualified for a special $1 price on a product. If the order total exceeded $100, they'd be shown a list of products to choose from, otherwise they'd only have 1 to choose from. Also, I'd be sure to include a 'No, Thanks' option.
I'd also use the NOTIFIER_CART_UPDATE_QUANTITY_END, NOTIFIER_CART_REMOVE_END, and NOTIFIER_CART_REMOVE_ALL_END observers to remove the $1 gift product if the customer's shopping cart drops below the minimum for having the gift and to make sure that they don't go round in a loop and add more than one $1 item. Probably also be good to have a check to see if they've started the checkout process with only enough to qualify for the one-option $1 item, but have subsequently changed their cart to qualify for a choice. Would then need to make sure that they go back to the page where they get to choose.
Is this making any sense?
BrandTim