The GBA supercards are also probably the worst choice of GBA flash cart. Find one on the street and it will allow you to do serious damage to the GBA library, can't really suggest it beyond that though.
Right now your main choices for GBA flash carts are
EZFlash 3 in 1. Used mainly with a DS flash cart. Cheaper than the others. Does not have SD card slots and relies on a DS cart to manage it. I don't know if any DS flash carts support SDXC offhand but you should have some space left over on a 32 gig card if you stick the GBA set on it (not sure what the extracted and trimmed size actually is). Personally I never got the desire to have a full set to go walkabout with but to each their own I guess -- the GBA has a fantastic library that will take you years to go get through at a vaguely sensible pace but why you would want to also have every region's copy of a trash anime tie in game I am less sure about.
EZ4. Prior to the everdrive it was the main GBA flash cart available. In recent times it added SDHC support and auto patching of games (which some seem to really like despite it being trivial to patch things).
Everdrive. There is the X5 model (
http://gbatemp.net/review/everdrive-gba-x5.489/ ) and the X7 set to drop any day now. They are more expensive than the others, however they are also slightly more featured. You can play just about every game with one, just like you can with basically any other flash cart which is not a supercard (or a clone of it). If you are not familiar with the everdrive peeps then basically where all the other consoles were messing around with old designs for flash carts the everdrive came in and designed things from the ground up using modern chips. As a result they now basically own the entire older console flash cart market (or at least all the big sega and Nintendo cartridge consoles and handhelds that were not the GBA). They also did it for the GBA a bit later but the GBA is pretty easy when all is said and done (no real major trip ups like NES mappers, GB/GBC memory bank controllers and SNES special chips) so everybody that wanted such a thing could play whatever they like as it would have be in an original cartridge, and had been doing so for many many years (I have a list of trouble games I link in these situations
http://gbatemp.net/threads/buying-a-gba-flash-cart-in-2013.341203/page-18#post-4756995 , everything else
http://www.advanscene.com/ worked fine really and most of those trouble things could be fixed).
"infinite saves"
Do you mean you want to be able to rename saves endlessly or just that everything needs to be able to save? The former was sort of a feature on some carts (not sure if the current EZ4 loaders have it but the older ones did) but it was buggy. The latter only really applies to old style NOR flash carts where you had limited SRAM and thus with large Flash using saves and smaller ROMS you might have been able to filly up the SRAM while the NOR still had space, I am surprised you found anything about that really.
As was mentioned the GB/GBC and GBA are different beasts. There was an older series of flash carts with an adapter but today it is GB/GBC flash cart or emulate it via something like goomba color (though if you are going for the 3 in 1 and a DS then the DS has nice GBC emulators too). The everdrive company makes a GB/GBC flash cart if you are going that way.