As far as how many plants to plant, I'd suggest planting heavily at first. I wouldn't be too concerned about exactly how many plants to get, just make sure you've filled the tank well. This will help with algae, especially if you use some fast growing stem plants like hoppy suggested - hygrophila especially.
One other item you've missed is fertilizers. With a non co2 setup you'll probably just need a good micro nutrient like seachem flourish comprehensive. And I'd dose once every week to two weeks.