The way that I see it you would have the store setup with three products. You would first have the family registration, then the individual registration then the raffle tickets.
For the family registration you would have a total of 6 sets of the options, each set would contain Name T-shirt-size Age Gender Race(5K or 1 mile), one for each member.
The individual item would be quicker to setup since there is only a single set of options.
The raffle tickets will be very straight forward since there will be no options.
Once you have added the products with the options you would need to modify the template. You should remove the left side nav and replace it with whatever you would like or leave it empty. Next you would want to modify the menu that lets you select the category, you would remove the category option and just link to the product listing page. From here the user can choose the product then on the details page they will be able to set all of the options and add the item to the cart, then proceed to checkout.