You should remember though that in order to achieve maximum growth of a heavily planted tank, you do need good lighting and careful fertilisation, and probably CO2 as well. You might not need all of these initially apart from good lighting, but as the plants continue to grow they might start to deplete the available nutrients in the substrate/water column being produced by the fish and if you start to see signs of deficiencies you might need to be prepared to add these in, so it's a good idea to do a little research and find products you think would work. It's a bit of a balancing act when you first set it up, but once you have the right balance you'll soon be having to trim them back weekly!
From personal experience, Seachem Flourish Comprehensive is a great product. Seachem produce a range of macro fertilisers as well but you would need to test the levels to add these effectively. You can also get combined macros which are a little easier to use. I found a small CO2 diffuser greatly improved the growth rate of my plants as well.
I happen to love duckweed... it is messy but you can easily scoop clumps of it out if they overgrow the top of the tank, and they do perform wonders for water quality. If you're trying to achieve a silent cycle then I'd at least consider it, since it's just about the fastest growing thing out there. Water wisteria is a fast grower too, as is anacharis. Hornwort is another one to consider. It's a good idea to float all the stem plants for a few weeks when you first put them in to allow them to get used to your water conditions before planting them. This will reduce the length of time they take to start regrowing after the initial die-back phase.