I looked into this a lot when I first got my card in August, this is basically what you can use:
DSHobro: not very good for general browsing, need to be running a server on your computer, only displays a static image of web-pages
Bunjalloo: best homebrew browser, can load images, but is a lot faster without them. gbatemp sort of works on it.
DSOrganize browser: not a bad browser, but the application corrupts SD cards
Okiwi: would have been good, interface looks good, but doesn't appear to be finished, as I couldn't get any websites to actually load
DSLinux browser: text only, and the OS will likely have memory crashes without a memory expansion
Then the official web browser, would be the best of all probably, if you got the EZ-3 in 1.
What did you mean by chat?