New Pond: need help selecting pond plants.........

Hi All,
I just installed a 220gal above-ground preformed pond in my
backyard. I know it's a little late in the season to be putting in
plants, but living in Louisiana I'm hoping it won't matter. I am also
building a small 30gal veggie filter. Now here's my first problem, I
put the pond under a large tree. I know this is not good placement, and
I will probably regret it in the fall. LOL. However it is also making
it hard for me to decide on plants to put in the pond. HALF the pond
gets filtered light/ some full sun while the other side only gets
filtered light / shade. So I'm just not sure what plants will do good
here. I really wanted lilies, but wonder if the can live here. Also was
looking at "elephant ear", the type for planting in the pond, and
something that would do well in the veggie filter, which is in partial
sun. I know I want things that are very easy to care for, and can live
with fish. I also don't have very much to spend on this, so if anyone
has a cheap online soure for plants, please post sites, and could you
list some plant types that would do good with my pond conditions.
Finally, is it very important how fast the water goes through the
filter? On My filter the water will come in at the bottom go through
lava rock / plants and then fall back into the pond via a small
waterfall. So the water will be moving kinda fast (I think, don't have
filter hooked up yet), is that OK? Thanks for any help, this is my
second attempt at ponding, My first (much bigger) one was always green,
so I just pulled it up when my daughter starting walking. I've always
loved ponds and hoping this one will stay nice. Ouida