Does the OS live in flash on a readonly filesystem? Do I have to build the OS image and flash the device with it, or can I ssh to the default install, load applications, and they remain there through reboots. I suppose the core question is, is the a read-only filesystem?
Also have some questions. What sort of Indians do I need?

Linux ARM big endian glibc 2.2.5
Linux ARM big endian uclibc 0.9.28
Linux ARM little endian glibc 2.2.5
Linux ARM little endian uclibc 0.9.28
In order of your questions...
No. No yes yes yes. no. Little/why-does-it-matter ?
Start reading the forums here and the wiki. It'll take a while for your sheeva to arrive (mine took 38 days) so spend the time surfing the forums here and the other sheeva sites/wikis out there. It'll help.
The system comes with a small Ubuntu 9 on it, mine was a pre-release, which you can use apt-get to update to current. The apt setup is good, there are a zillion pre-built packages already available for download. My recollection is the sheeva is little endian if it matters, but the apt-get method gets the right stuff regardless for me.
The flash is 'not' read only, you can (and should) update it but be aware it's jffs2 so it's slow, and the size is of course very limited. I updated the kernel to 2.6.30-rc7 from the instructions in the kernel forums here, verified it was good, then copied the rootfs over to a ext3-formatted 16GB SD card. The speed increase is 'amazing' if you do that.
Now that I had 15+ GB free space, I used apt-get to install gcc and all the other things I needed to compile the wview weather station software I bought the sheeva to host. Other than wview itself, which has no debian installer (yet) I have not had to compile anything on the sheeva. Works great so far.