perusing
virgin coconut oil is one of the easiest to swish with (olive oil just has a very distinctive taste...and I don't like how it draws up mucus piecemail as opposed to castor oil which for me brings up the mucus in one big solid blob or two.)
coconut oil is also the most diverse-- used topically, internally, for cooking, or oil pulling.
Oregano oil is a must for times you come down with a cold. It also did wonders to dry out or bring to a head certain deep zits (like Vitamin E oil) that may make a fan out of your child with acne. watch out with sun exposure with oregano oil though-- you don't want to wear it out or it could make your skin turn darker permanently (hasn't happened with me but I wear it as a mask and wash it off or wear it over night.)
other than that-- it's up to you. you haven't specified any maladies that would need any of the omega 3-6-9 oils like flax seed or hemp, so just slowly expand your oil selection and become an OP connoisseur!