For SH4 (I cannot speak to 3) there are a few mods out there that I would consider.
1. Run Silent, Run Deep the Campaign (RSRDC). This mods the PTO campaign which is horrible in the stock game. I consider RSRDC to be obligatory.
2. Trigger Maru Overhauled (TMO). A total mod of SH4. Eye candy, realism, and even a campaign that is better than stock. There is an RSRDC release that also works with TMO, so you can do TMO+RSRDC. TMO makes the IJN ASW considerably more competent, though the ReadMe tells how to adjust this down if you wish (perhaps a good suggestion for your first patrols). Excellent mod.
3. Real Fleet Boat (RFB). RFB is, like TMO a total mod of SH4 into something playable. Eye candy, sinking, etc., just like TMO. Their focus is more on realism so ASW is easier than TMO. RFB has no organic campaign, so you'll need to run it with RSRDC.
4. Fall of the Rising Sun (FotRS). I have not played this. It is, I think, based on TM, but with a large campaign.
Outside the PTO:
5. Operation Monson (OM) is available by the author of RSRDC (lurker) for the ATO. It is as compulsively accurate as RSRDC is. I've never played a U-boat, so I am not the best judge.
6. We Dive At Dawn, also by lurker is Royal Navy subs.
7. There is a mod that looks to be pretty cool call Battle for the Baltic as well.
So I'd start with TMO or RFB plus RSRDC. Some will claim stock is good to mess with, if for no other reason that to appreciate the mods more. I think the stock campaign is unspeakably bad, myself. I'm a bit of a grognard, however
