200mhz 64MB ram. It's on 1GB CF card. And i have usb so external HDD or larger USB key could be used for download for example in the future.
i have tested my solution with the "mydata.tce" file which could work for you even with these hardware specifications:
0. you have to boot tc ones and to specify most of things the first time in order to have the look&feel that suits your needs (wallpaper, options of apps, filetool.lst and bootlocal.sh);
1. download (preferably tcz) your apps, choose gtk-1 and cli apps if available; you will install them once you will use them (not at boot, but from the appbrowser);
2. backup your system on an external device and reboot; you will have a "mydata.tgz" file on your external device;
3. at the reboot, enter: tinycore norestore <--- as well as other parameters if you need them depending on your computer (f.ex. waitusb or swapfile; in the bootline, enter: tinycore swapfile waitusb=10 for example);
4. once in tc, rename your "mydata.tgz" file into "mydata.tce", and load mydata.tce with appbrowser; in order to see the changes, do: ctrl+alt+backspace, and once in the console, enter: startx at the prompt; you should face your customized system; after that, you can install your apps.
* advantage of this solution: you don't need to restore your backup file at boot which allow low-ram machine to boot without too much trouble (even with some extensions loading, such as fonts, mc, beaver and so on);
* disadvantages: if you change your preferences (say, if you want another wallpaper, or if you use sylpheed mail in order to get your emails), you have to backup your system at shutdown, and to rename your "mydata.tgz" into "mydata.tce" once you reboot your system. Anyway, like a lot of low specs machines, these are usually use for specific tasks (such, as you said, browsing the web, chatting, emailing etc.) so that normally, you won't change your customization much, and then this solution can work well for you.