Yeah if you are used to no$gba, fceux, vba-sdl-h and such like then moving to later consoles can be a pain. I have not really taken the DC to a high level but hopefully I will be able to point you somewhere for the time being. Several emulators will have GDB stubs/support, lua scripting and whatever else but I am not sure what goes here (lxdream has a measure of GDB support).
Most will usually flank them with with cheat making tools like emuhaste and artmoney, the former seems to have nullDC support (though it might need a tweak for newer versions) right out of the box and the latter seems to be a favourite among DC cheat makers. Both programs actually afford quite high level abilities when it comes to making cheats but proper breakpoints, stepping and whatever else you are used to with the high level stuff is not so doable. Memory dumps are easy enough though.
A lot of the rest of the time it amounts to messing around with something like IDA as well.
Basically anything that is not a NES, SNES, GBA, PC or possibly the DS you will have to wing it using a combination of all sorts of tools (read static disassembly and cheat making tools) if you want to do anything more exotic that make cheats.