Congratulations on your engagement and your success in school! It takes a lot of tenacity to do that with little ones.
Ok, to the subject at hand...Tile or Bamboo have my vote.
Pros for hard floors -
Cleaner than carpet
Better for health
Last longer
Easier to clean
Carpet harbors dust mites (major allergy producers!) and dirt. With all your pets, you'll have a really dirty carpet pretty quick.
Hard floors are easy to clean. Get a microfiber mob with extra cloths (Lowe's or Home Depot's are priced nicely and hold up well) and just wipe it along the floor daily to keep the hair problem at bay. When you're through, throw the mop in the washer. If you buy the extras you'll always be able to grab another when you need it. Easy and eco-friendly.
Another pro about getting rid of carpet... Your house will stay cooler! Carpet holds heat.
Bamboo is very tough (if you get a good brand - we have EcoTimber) and will hold up to pets/kids etc.
Have fun shopping!! :)
M.