A great alternative to Ydiss's suggestion is the Python. This is a truly great medium sized all rounder with very few limitations. One of my go-to ships even after 4 years of playing. It's a beautiful ship to fly! It can fit a fighter bay too. But personally, I don't bother with fighters any longer as I feel they are not worth the time and cost of a size 5 bay.
The Python actually cannot fit the fighter bay, it's the one significant trade off as a multi role fighter. I'd also never suggest someone use the size 5 bay as the loss of a fighter (which can happen even if you're careful and your crew is elite) means 80s downtime. I agree that's not worth the 5 slot and definitely not worth the crew upkeep (in my opinion).
The Python is a very capable combat ship. Just not something I'd recommend for the dedicated role which seems to be the op's requirement. It's a fantastic option for running missions of all types and can be fitted to fight back. It's more flexible, is the best passenger ship (Robigo) and can carry the most freight for a medium ship.
For raw combat, if you want the best, it's just not agile or fast enough. The krait mk2 beats it in those areas and can fit a size 6 fighter bay, which is awesome. It's literally an additional large overcharged, oversized multicannon (and then some because it's higher dps than that and the fighter will hit your target even when you're turning) with no ammo requirement and the additional benefit of distraction. That's enough to render the battle between the two as pure combat moot (they have the same hard point layout and very similar internals).
But for mixed role, I agree it's a fine choice and used to be my favourite ship for that. Just love my Krait mk2 too much now
Edit: There are better pure combat ships than the Krait but I'd argue it's right up there for its size class; none of the other medium ships can fit an SLF size 6 without sacrificing shield strength, except the Gunship which isn't one I've tried I'll admit but that's because it looks too slow and sluggish for my tastes (and is rank locked, might as well just go for the Corvette imo). And that, in my experience, is worth a lot. Nothing beats the defensive capabilities of the large ships of course. But I find medium ships are just as fun and can take a beating if you stack guardian shields. That does include the Python, I'd just say that's if you want to do other stuff too (which I'm sure will be useful for the op).