Rainwater will work great for your DWC. I use it on all my hydro setups. I checked it with my meters and it read 7.0PH and 60 ppm, which I think is mostly sediment from the roof. Filtering with a t shirt is a great idea, but not necessary for DWC. No other purifying is needed.

When using rainwater (which is nearly perfect as it comes, but) please consider that unlike tap or well water, it has literally none of many secondary elements (Ca, Mg, nor Fe, B, Na, Cl, Si, etc) that originally come with the other waters. Hence use nutrients that provide enough Mg and Ca in the first place and adequate amounts of minor and trace elements. For short term species, leafy vegetables and herbs (if short term) and micro greens and lettuces, the lack of "minor but beneficial" elements and trace elements may not lead to deficiencies or "health issues", etc - but with tomato, peppers and other long term crops, it would be a good idea to use (look into) some complemental nutrition product that provides the above listed "minor elements".

There are specific components and "raw materials" as well, that can provide those - but that's only of interest if you make your own nutrients and/or if you know perfectly well how to use and dose them.

Thanks urban and lucas, my rainbarrel collects more than I can use so I thought it would be good to make use of it. I plan on using Advanced Nutrients GMB. I've had good success with lettuce, but now on to peppers and toms. Any advice on nutrient mix or just follow the label.

Thanks again

As I said earlier lettuce and related aren't very demanding, or let me put it even that way: lettuce (and some other) grow with various nutrient compositions even if they are deficient somehow. That is one of the reasons why so many people are successful with lettuce (but with various formulas) and I also believe that this is why it is so widely cultivated commercially (with hydroponics). Here in Thailand we use to say "pak salat kin mot" - lettuce 'feeds on' anything!

Tomatoes and especially peppers are more demanding though and the minor or missing quantities (due to mineral poor rainwater) will play sooner or later. First of all, look for a "soft water formula", which in fact has higher Mg and Ca content. If I remember well, some manufacturers (GH?) do offer exactly these soft formulas. Also, choose a formula with high potassium content. Generally N to K ratio around 1 to 1.5-1.8 (2). Do not fall for any high phosphorus formula for bloom or whatever. This concept is old school and OUTDATED.

Unfortunately I cannot recommend any specific product(s) here, as I am exclusively using (my) self made nutrients, - but others can, may and probably will ;-)

PS: peppers and toms haven't got exactly the same nutrient requirements and need slightly different concentration also. Well, it depends on species actually. They both grow well under a PH around 6. Here again, I recommend to get it slightly under 6 and let it fluctuate until 6.3 with a max of 6.5, before correcting or changing nutes. Bell peppers (compared to hot peppers) can be feed with higher EC and will be happy from 1.8-2.2 EC which would be the compromise for peppers and toms, I'd suggest anyway. With other species like various hot peppers, keep EC under 2.0 (1.5-1.8 is ideal) if possible. Actually, most peppers could use somewhat more Nitrogen, while toms tend to have too much vegetative growth and bloom late with too high N levels. In my experience, a good compromise for both is between 160-180 ppm of Nitrogen and at least 250, or even better 280-300 ppm of Potassium. Some manufacturers have nutrient calculators and with those you can try to find (and use) a mix that is close enough to these specs, which you can find confirmed on other (the right) places.