Is she old enough for a lunch box of stuff she can choose from during the day? Pack it with what you want her to eat and let her chose a thing each time but don't get anything else for her.

I don't really worry about veges. None of my kids have been keen but they eat a load of fruit so I figure it balances. At 7, DS will now make a hamburger with lettuce and capsicum (no meat lol), At 5 DD1 has just realised she likes potatoes. It will come. It is always there on the table and we offer it to them. Every now and then they will try it.

My suggestions for less messy foods include plain pasta, cruskits, sandwiches, toast (folded in half), cut up fruit, crackers. Have you tried frozen mixed veges? Mine liked that when they were about that age. Also cheerio's (while questionably meat) are fun to eat if you have sauce for dipping