I think it was Blue Emu showing repeatedly in playthroughs that you certainly can successfully wage a sub-war against convoys. And for this the standard subs are cheapest and best.
That having said, I must admit, usually I went a different route as Germany when it comes to seawarfare. I built and used Heavy Subs and equipped them with float planes. Planes on subs look somehow crazy and the Germans did it only with very few subs (the Japanese, building much bigger subs, did it regularly, though). Fleets of HSubs/floatplanes, especially in the beginning of the war, are deadly and I used them to directly hunt down more or less the whole of the Almighty Royal British Navy. Once sea-superiourity is achieved I switch to CVL and DDs to escort my transports to... well, all over the world. Venecuela is a nice target if you don't want to bother anylonger about oil.
If you want to be somehow "fair", don't use bigger stacks than 6 HSubs.
One should make sure to start the war with 24 or more HSubs, though, with at least 6 different serials of ongoing production. You'll loose some HSubs, they'll get damaged all the time and you need to call them back to port very regularly. 6 or even 12 serials of HSubs look a lot but they are really cheap and also rather fast to build, roughly DD cost. And you aren't (shouldn't) building anything else pre-war. Using more than 6 HSubs in a single fleet makes the game boring, though. And since 1 HSub in DH stands already not for one sub but for several, it is also kind of unrealistic having the waters swarm with hundrets of them in a small area.
This means you are going a different route than in history. Dictators (and Kings) seem to have an unhealthy love for "Oh, let's build the biggest guns!". Historically Germany went with a surface fleet... which wasn't really that much in comparison to the British or French. And the nice expression "fleet in being" means
a) they found somehow a kind of strategic reasoning for why having those expensive BBs and BCs at all
b) it also meant better for those ships not to leave the harbour.
The relatively small German fleet had been quite shot too pieces right at the beginning of WW2 by... Norway and in the direct aftermath on their way back by the Royal Navy. If I remember correctly more than a third of the German fleet was lost. As hinted at already above, the actual legendary sub-war was rather something not initially planned and then done out of necessety because no other means were abailable. It took a while to get implemented and then the subs needed to be build and that late the subs were, as successfully as they partly were, always fighting an uphill battle and the allies not only having enough time to develop counter-measures technically (radar) but as important tactically (convoys, small convoy aircraft-carriers etc.). Do it early and with sufficient numbers, if you want to have a similar effect at seas like with lightning wars on land.
What it historically shows, not really surprising, as much as the whole German military sat down to think why they lost WW1 and what they'd need to change in WW2, the vast experience the Germany military had in landwarfare it lacked basically completly in seawarfare. Just look at the fate of the Bismarck, a remarkable ship when it comes to BBs, true enough, but no British Admiral would had ever been as stupid as sending one lone BB accompied by one lone BC into the sea, no DDs, no support, no recon... but with really big guns.
I almost forgot: Don't build only subs. Build also some transporters. At least if you want to conquere the UK or anything else not reachable via land. Another thing the great German admirality... forgot.