Neither denn nor dadurch is redundant. TLDR version: denn dadurch translates to for by that.
Let’s see what happens if we leave either one out. First we drop denn:
Am liebsten wäre mir ein Girokonto, dadurch hätte ich die Möglichkeit, alles per Scheck oder Banküberweisung zu bezahlen.
This is two main clauses in a row. You can do this, even without joining them by und, but then you should separate them by a semicolon. (Or by a full stop/period, of course.) If you really want a comma, you need to transform the second sentence into a relative clause:
Am liebsten wäre mir ein Girokonto, wodurch ich die Möglichkeit hätte, alles per Scheck oder Banküberweisung zu bezahlen.
That’s just like in English, except in German the word order in a relative clause is different.
Now we drop dadurch instead
Am liebsten wäre mir ein Girokonto, denn hätte ich die Möglichkeit, alles per Scheck oder Banküberweisung zu bezahlen.
This is not even grammatical. German denn is a bit of a false friend because the German word for then is actually dann. (Even worse: In antiquated German you can use denn for comparisons, in the sense of than. So the roles are precisely reversed!) Without dadurch, we need dann, not denn:
Am liebsten wäre mir ein Girokonto, dann hätte ich die Möglichkeit, alles per Scheck oder Banküberweisung zu bezahlen.
But this is still not quite correct. As in the case of dropping then, we now have two main clauses in a row. We should separate them by a semicolon, join them by und, or just use a full stop.
Or another way of fixing this would be to join them by denn:
Am liebsten wäre mir ein Girokonto, denn dann hätte ich die Möglichkeit, alles per Scheck oder Banküberweisung zu bezahlen.
You might think that denn dann feels as weird as a duplicated word, but it doesn’t. In fact, it’s a very common combination of words that translates to English for then. And indeed, the standard meaning of denn is because or for (the one that means the same as because).
In your sentence, dadurch isn’t very good style. It feels a bit colloquial here because it’s not clear whether you mean durch das Konto (colloquial because standard would be mit dem Konto) or durch den Besitz eines Kontos (colloquial because the noun this refers to never appeared explicitly). It would be better to use damit, standing for mit dem Konto. So this would be slightly better:
Am liebsten wäre mir ein Girokonto, denn damit hätte ich die Möglichkeit, alles per Scheck oder Banküberweisung zu bezahlen.
Except, of course, for the idea to use cheques. In German-speaking countries, you would normally only encounter a cheque if someone wants to annoy you or doesn’t want you to receive the money. (In the last decade I have seen precisely one cheque while living in Germany and Austria. It was some kind of bonus from my health insurer. I am sure I wasn’t the only recipient who didn’t cash it. I had no idea how to do that given that my bank doesn’t even have a normal branch in Berlin. The effort of figuring this out simply wasn’t worth the 30 Euros or whatever it was.)