When your child can follow simple directions, have him pick up all the food he throws on the floor, and place it in a small portable trashcan/sack. It doesn't deter him from throwing food on the floor since the cleanup is still fun, but it is a start to learning there are consequences for his actions. My son is 20 months, and we also have him "help" us put laundry from the washer into the dryer, and he "helps" put his toys up into the toyboxes. If I am cleaning something that involves wiping, sometimes I give him a washcloth so he can feel like he is helping to clean too. It gives him a great feeling of accomplishment, and is great training for future chores.

For a first birthday, when I don't know what the birthday kid already has and the child might rather play with the box than the gift, I like to give useful things. Here are a few items that I think would be great gifts for a first birthday:
 - Diapers- size four or larger should work (perhaps a diaper cake)
 - Wipes- yep, still need these
 - Boogie wipes are great too.
 - Toddler toothbrush and toddler toothpaste
 - Clothes- size 18 month or 2 year, keeping in mind the season when the child will be that age.
 - A training potty
 - Pull-ups, underwear, potty training books, or other things relating to potty training. The parents/child might not be interested in potty training before the 2nd birthday, but these items would be nice to have when that time comes.
 - Baby food, healthy snacks, and feeding accessories like feeding bibs (the wipeable kind that catches food) and snack travel containers
 - Sippy cups. We can't seem to have enough of these.
 - A gift certificate for professional portraits might be a nice idea.
 - Baby wash, shampoo, lotion, and cotton swabs are things that often need replacing.
 - Shoes, I would go with size 6 to be on the safe side, but size 5 might work. For this newly walking stage, I strongly recommend flexible soles. I loved my son's Pedipeds (available at USA Baby, boutique baby shops, and ebay of course), which lasted several months. They are a little pricey (for my standards at least) at about $30, but I am really glad I got them.
 - House slippers- cute and functional
 - If you are creative, have time and access to a bunch of photos of the baby's first year, a photo book would be a great gift. I have made a few with Shutterfly that I am really happy with. A gift certificate for mommy to make a book with Shutterfly or comparable book maker would also work.
 - A collection of books with the child's name in the title would be fun. I came across a website called More Than Paper where a book can incorporate a child's name, friends, hometown, etc.
 - Last but not least, I can create something unique for a first birthday gift. I have the froggy potty gift and two gift basket examples in the photo gallery- the orange crate with diapers, sock monkey and other frequently used items, and the blue container with food and feeding accessories :)