Yes, you can play clean (unpatched) DS ROMS with the slot-1 solutions, but not GBA games.
The most important thing is to get a good flash card. Portrait of Ruin is an example of a recent game that is very picky about which card is used. The game causes lock-ups on many flash cards. The current popular pick is the Kingston/Toshiba 1 GB microSD card (SD-C01G SDC/1GB). The problem is that these cards are either assembled in Japan or Taiwan (the sticker on the back of package will say "ASSY IN JAPAN"). The ones from Taiwan are crap, the one from Japan are near perfect. I was using a San Disk Ultra II card in a slot-2 device and didn't have any issues with any game until Portrait of Ruin. When playing PoR the game would freeze on me from time to time. Once I got the Kingston card, it never locked up again.
This site
here actually sells the two as a package and specifically advertises that they are the Japanese cards. I've haven't seen the cards sold in any local stores, so I had to buy online. The problem is that most places won't promise to send you a Japanese card, so you just have to order and hope you get the right one. I bought two from Meritline.com for $10 USD each and both were Japanese (they are currently selling for $14). Of course, I see you live in Australia, so I'm not sure where you should buy from.
Hope that helps.