Firstly, why would you need 2 tanks? Just run it through a DI on its way out to your van or wherever else you need to use it.
Rain water is very pure, but by the time its ran down the roof and along the gutters it will have dissolved a fair bit of impurities and picked up some grit etc so yes a sediment filter on the way into your storage tank is the way to go. Unlike tap water, it has not had chlorine treatment so it will be prone to algae growth if left where light can get in.
It's also worth remembering that pure water doesn't stay pure forever, even if it's just sitting in a tank the TDS will slowly rise, so this is another reason to have DI on the way out.
Personally, I think this is a lot of trouble to go to just to 'always have pure on standby'. Rain is also unpredictable, especially in the summer months, so you'd need quite a lot of storage capacity to make that work.
Its much easier to just produce your pure water as and when you need it with an RO system. That's what most people do. I worked out the cost of producing pure water a while back, and it was about 0.2 pence per litre or something, not worth worrying about and certainly not worth the effort of devising some kind of other system to avoid the cost, especially when you compare it what can be earned with that pure water.
However, if there were ever a drought order though, you'd be sorted. You could continue to work and smugly point at your rain-water harvesting system if any council busybody jobsworth tried to stop you. Mind you, that only happens about every 30 years or so.