I have done both, more GBA than DS. I would recommend GBA first then moving up to DS because it doubles the complication. The ezflash V gba sized 3 in 1 is a good card. I have a bootloader for the gba that I wrote to the card using an NDS and a program that I downloaded that I cant remember the name of off hand. Once the bootloader was working a serial cable and lets me debug programs as well as load them into ram. that card also allows you to load into ram on the card and run from there taking advantage of the prefetch buffer and a bigger program. For the NDS I have tried many of the cards. The cyclods is good for day to day use, but for development not so much. I think I liked the Acekard 2 better, or the R4. think about the number of times you pull the card out and pull the sd card out and load it into a computer. Very painful you want a card with an sd card slot you can get at without having to pull the slot0 card out. the cyclods is not it. A very good card though for the NDS. I dont think it works on the NDSi where the acekard 2 does. For both nds and gba you can get your feet wet with simulators like visualboyadvance, they are not completely accurate and very common that programs that work on the simulator will not work on real hardware, programs that work on real hardware will usually work on the simulator though. removing the development card, reprogramming, and replacing is very painful, bootloaders, wifi, or any other way you can avoid that is well worth it.
Arduinos are fun and interesting, the lilypad and the usb to serial thing is the one I recommend, no soldering required and you can start using for not a big investment. I like the armmite pro better, arduino like footprint but arm based (the only lpc I would buy, not an lpc fan right now). And you dont need to buy the serial thing, just a normal usb cable and a jumper (well maybe a paper clip until you solder on a jumper). I just ordered two more and so far my code that erased the as-shipped flash and allowed me to load whatever I want isnt working, gotta go figure that out. I continue to be very pleased with the olimex sam7-h64 and h256 (header board at91sam7s256), as with the avr atmel is very developer friendly with good docs. Sparkfun is a good place to find all of the above in the USA. Sam-ba now has a linux version if you use linux as I do, the windows version had been there for a while, fairly easy to erase and reprogram, much easier than a ds or gba, on par with the arduino or armmite pro or similar.
Formerly luminary micro now ti stellaris has some good boards. like the gba/nds but unlike the other boards I mentioned there are displays and other peripherals to play with, usb is all you need to program. thumb mode only though. GBA prefers thumb mode for performance but can go either way. nds, I dont remember, never got so far as to understand the width of the busses and their timing. Knowing Nintendo and their cheapness thumb is probably better/faster. the lm3s811 eval board was too easy to brick, the 1968 is not a bad one. I dont like that they were pushing developers away from the source and into pre-built libraries tailored to the rtos and specific compiler suite.