Many people do start solids at 4 months (the AAP recommends waiting until 6 months, as of course you know). It is totally fine to start solids slowly (probably better in fact, because it gives their tummies time to adjust and helps prevent constipation). Stick to gentle stuff like pear, banana, apple, mango, plum, avocado, and peach.
It is a myth that you need to do veggies first in order to get them to accept veggies; all sources I have read say either fruits or veggies first is fine.
Even at 6 months you should count on BFing (or formula feeding) for most of their nutrition, and at least 4-5 times a day. Even at that age most babies are only having 1 meal of solids (like I said, no need to rush), and breast milk/formula remains the best nutrition until 1 year.
A great website for starting solids is http://www.wholesomebabyfood.com