algae is a funny one here's my best basic explanation
to get plants to grow you need lights, nutritents and Co2. obviously the lights are extra equipment although if the tank is in direct sunlight this will contribute too. There will be some nutrients in the water (think of the fishy poop as compost) and there is naturally some Co2 in the water anyway.
algae will also grow when the three things above are in good supply. algae is less demanding than plants. If you imagine quantifying the lights, nutrient and Co2 so for example you had 5 units of lighting, 4 units of nutrient and 3 units of Co2. your plants would use up the 3 units of Co2, 3 units of nutrients and 3 units of lighting, because there's only 3 units of Co2 they can't use the excess light and nutrients. The algae can grow without having lots of all 3 in place so they will use the extra units of lighting and nutrients and as such you'll get algae growth.
now it doesn't really work like that in practice, you can't always easily quantify the levels you have and different species of plants and algae will have different requirements. but it serves as an example to explain the theory.
so amongst those fishkeepers who are serious about plants they normally go down one of two routes
they either provide so much of all 3 that the plants grow so fast and use so many nutrients that the algae doesn't get a look in, or they provide a low level of all of them, then the plants use it all and you just get steady slow growth. really the second option is what most average fishkeepers aim for.
in short what i'd recommend you do is get a good few bunches of plants in there, if you find you're getting a lot of algae growth try turning the lights on for fewer hours a day. it's a bit of a balancing act really but just tinker with things and you should find a happy medium where you just get a little bit of algae (cos really, we all get some).
regarding new plants and decor, add them when you like, doesn't make any difference.
don't worry about keeping the old tank set up, if you've room to store it then keep hold of it so that you've got a spare tank incase you ever need it. cos you've got a mature filter all you'd need to do to set it up again is add water, move the filter over and then mvoe the fish over.
