You can find a list of the animals in Harvest Moon (GB) here.
Both animals can be fed fodder, chickens are not fed chicken feed just like in SNES. They both also stop giving produce if they are not fed for a day and will continue to not give any produce for three days.
Chickens- These will be potentially the first animals that you get. They produce eggs everyday if taken care of. They require minimal care which just involves putting feed in their box. The barn is very small, so it is very easy to get trapped by the chickens when carrying an egg or feed. Put an egg in the incubator and a chick will hatch.
Golden Chickens - There is a 1/64 chance when you trade a chicken that it will be a Golden Chicken when you get it. Golden Chickens will lay Golden Eggs, which sell for more than regular eggs.
Cows- Bringing more of a profit, there are cows. Beyond just giving them food, they require more care. Brushing and using to take the cows out on a walk on sunny days will make them happy and produce higher quality milk. Also, you will need a milker so that you can get milk from the full grown cow. Pregnant cows cannot be milked. You can impregnate your cow with a miracle potion and in 21 days a calf will be born. Cows will also sell for more depending on how big the milk they produce. Butter and Cheese sell for even more when you purchase the makers.
Blessed Cow - If you pray at the Church for 10 days straight, the Harvest Goddess will bless one of your cows. Once they are blessed, they will never become unhappy and will start giving Large Milk immediately. You must have a cow fist, though. It is unconfirmed if it will ever get sick, but it most likely won't, if it doesn't even get unhappy.
Horse- This animal, unlike the others will not give you any profit. On the 10th of Spring on you first year it will appear. It doesn't require any care and just roams around your farm. It will grow up and then can be used as a portable shipping bin.