It's good advice to suggest a larger K-frame as a first revolver - BUT - the op seems to need a dual-purpose revolver for both carry and home defense. Therefore, his own suggestion of the .357 LCR is a good one that meets all his criteria.
The LCR was designed first and foremost to be a carry gun. So, it's much easier to integrate into a carry routine than a larger and heavier revolver that may be nicer to shoot, but bulkier to carry.
It's true that shooting hot .357 Magnums from a lightweight snub nose involves a lot of recoil, noise, flash, muzzle flip, and slow follow-up shots. It may be too painful for many shooters and in an enclosed space such as a home defense situation, the noise and flash can blind and deafen you at a critical moment.
Still, that does not mean the OP has to carry hot Magnums in his LCR. There is enough variety of power levels in both .38 Special and .357 that everyone should be able to find effective loads for practice, carry, and home defense. You could do a lot worse than 148gr .38 Special wadcutters for practice and Speer Gold Dot .38 Special+P for carry and home defense.
The ability to shoot .357 is still always there if you happen to wander into bear country or maybe you just want a little more thrill at the range.
The LCR is also reasonably priced, widely available, and unlike the suggested used K-frames, you don't have to worry about the history and condition.