I asked Ian at Tuffsaws the same question and of course there is no one blade that will cover all bases, but he recommended a Supertuff Premium 3/4 vari tooth, which has sections of three teeth and sections of 4 teeth, but it will only really go down to about 10mm thickness. To cut really thin stuff like your 3mm, you need many more teeth as there need to be 2/3 teeth in the wood all the time. Don't know if they do them in 10mm wide but some of their blades are easier to tension than others ( thinner gauge metal) and you can go wider than you normally can on your bandsaw.
Something like a 3/8", anywhere between 6 and 10 teeth may also do you as a multi purpose blade but as i said, there isn't a one blade fits all scenario.
You could ask Ian, he is very helpful.