Small birds are wary of predators so plants that give them cover are as
attractive to them as those that provide food. I have introduced Hebe's to
my garden and they are always full of birds, it may help that I grow Verbena
through them and they love the long stems.

I also have three feeders, one for peanuts, one for seed and one that I made
for feeding meal worms to robins - but the sparrows like them as well!

As others have said your big tree is going to limit what you can grow and
the aspect (direction the garden points) will also dictate your success as
most plants need access to direct sun at some time of day.

Keith