Can I give customers a few options of free products to choose from?

Yes, you can provide as many options as you like.

To achieve that you need to choose ‘One of the SKUs below’ in the field ‘Type’ and specify the SKUs in the Promo Items field.

Bear in mind that the number indicated in the Discount Amount field is applied to the rule, i.e. if you set 1, then a customer will be able to choose only one promo product from the multiple SKUs you’ve indicated; if 2 is specified, then 2 free products can be chosen, etc.