What Your Rabbit Should Eat
Your rabbit's diet is very crucial to the longevity of their health. It is absolutely necessary to feed your rabbit with fresh water and Timothy Hay, not alfalfa. Alfalfa is okay to give to young baby rabbits, but only for a very short time because it contains such a high concentrate of calcium. Too much calcium thickens a rabbit's urine and causes bladder infections, kidney stones, and other urinary tract infections. So, Timothy Hay is the way to go and should be available at any pet store.
The next thing to put on your bunny grocery list are pellets. I can give you a few suggestions, but it is also up to you to read the packaging and make sure you're not buying "candy" pellet food. I recommend you not buying any sweets, and sugary toys for starters, instead look for a brand like Oxbow, (available at most pet stores). Oxbow has come up with some healthy gourmet pellets for small animals. Take a look at their nutrition label if you want to compare and supplement it with other generic versions.
So pellets and hay are the basics. Now, anytime you introduce your rabbit with other foods like carrots, apples, lettuce, and bananas, please keep in mind that a rabbit's stomach is very delicate. Having sporadic new foods is not a healthy meal unless you introduce it to your rabbit slowly, regularly, and with very small portions for starters.
Make sure not to over or under feed your bunny, however it is fine to replenish the hay tray regularly. I cannot stress enough that hay is a necessity in a rabbit's life. Rabbits are constantly grooming themselves and since they do not cough up their fur like cats do, it is imperative that they have hay to help push the hair through the digestive tract.
So let's recap: give your pet a balance diet, introduce new foods in small proportions regularly, and be sure the bun has plenty of hay and water.