Gameboy aka GB
Old monochrome device. There is also the gameboy pocket which is a smaller version of the gameboy with no significant feature differences beyond that.
Gameboy Colour aka GBC
Has a colour screen.
Has some limited colours, backwards compatible with all GB games. There are GBC exclusives and there are carts that gain features for being in a GBC. There is a very rare and hard to come by version of this with a lit screen, most you find nowadays will be third party mods.
Gameboy Advance
A fairly different machine to those before it. The original gameboy advance and gameboy advance SP can play all GB/GBC games too. The GBA micro can not play GB/GBC games. The DS and DS lite also have a GBA slot and can not play GB/GBC games.
The GB/GBC carts use 5V where the GBA uses 3.3V (look down inside a GBA and you will see a little leg that gets pushed down to activate the mode) so you can not simply dump GB/GBC stuff using GBA hardware. You can do a hackjob on an old thing from 2) in the list above
http://mootan.hg.to/fmgbx/ez_fmgbx.html and the same site as before also has a GB/GBC section
http://reinerziegler.de/readplus.htm#Home made programming systems , not sure what really exists commercially at this point in time and if you go hunting around you can probably find some GB/GBC save dumping setups made using an arduino if you prefer to go that route. I don't know if there is any kind of multiboot for the GB/GBC you could do like you can to dump GBA games.
Yeah the DStwo would be way overkill for just dumping games, it is a lovely cart but way surplus to requirements. I would get a reasonable DS flash cart though because if you are going into all this then you will probably want to play DS games eventually, if it was an extra $40-80 like it might have been for some things in the GBA era then yeah it is a decision but this is an extra $10 at most and if you are dumping your own games it is probably a vanity project anyway (you might have some saves you really want but probably not and thus you can just download them, nobody cares or gets arrested for it and doubly so if you do it properly) so just spring for it. I don't know what we are suggesting these days but the R4i gold was when I last looked and will do this happily and play basically all the games. Real time menus means basically nothing, or more likely that it has menus that you can open in game to select cheats (the DStwo also has that feature if you cared). The only thing that stops me suggesting "basically anything" is that some stopped updating before the end of the DS commercial library so not everything will play every game, and this does include big companies like EZFlash (their EZ5i stopped being updated and now things like pokemon typing and pokemon conquest are harder to play, not sure about black and white 2) and M3. Even of those weaker ones then most will play most things in it (there are not too many that were dropped in 2009 or something and not brought back in one form or another) though so it is not like you are going to go short of games.
I am not sure what shops we are suggesting right now either.
