B.C.
Hi A.!
Bananas, avocados, and cut up baked sweet potatoes are all great finger foods and very healthy. My one year old loves all of them and will eat them straight. My 2 year old is getting pickier, and will only eat them if she can dip them in something! (Avocados get dipped in ketchup or steak sauce, bananas and sweet potatoes I let her dip in plain yogurt with a little maple syrup mixed in.) Somehow being able to dip her food in something greatly increases its appeal--but whatever works, right?
I bake a couple sweet potatoes ahead of time--45 minutes in a 475 oven-- and keep them in the fridge.
Hard boiled eggs are another good toddler food- I cut them into quarters for my 1 year old. You can make these ahead of time, also and store them in the fridge for up to a couple days. I would recommend not taking them out of the shells until you are ready to serve each one. I put the eggs in the pot with the cold water on high heat--When it comes to a boil, turn the heat down to med-med-low and simmer for 12 minutes. Then pour out the hot water and fill the pot with cold water to stop the cooking process and get the eggs cool enough to handle.
Good luck! Introduce as many healthy foods as you can (like broccoli!) as EARLY as you can. I learned this lesson the hard way, and have had a lot of battles with my 2 1/2 year old. My 1 1/2 year old got a much better start with food and I haven't had near the struggle!
Edited to add: I know fresh vegetables are best, but frozen is the next best thing and can be a lot more convenient. I buy the bags of frozen organic broccoli florets. I turn the oven on broil, put a handful of broccoli on a foil-lined cookie sheet, and broil about 4-6 minutes. Then I squeeze the soft, mushy florets off of the stem before serving to my little one b/c she doesn't have enough teeth to handle the stem yet!