I agree about 'I' names being lovely - I have a soft spot for them to but Ida is far from my favourite. It sounds like when people say 'I woulda' very fast and it comes out like 'I'da...' However, I adore Ira for a boy.
Ida Caroline is a beautiful combo though. I adore it.
Other 'I' favourites:
Iris
Ivy
Iseult
Isabella (so generic, I know...)
Isla
Iona
Islay