If you meet a DVI-only device you can use a converter. VGA <-> DVI converters exist.

I'm not sure if I/O is important for Texrat, or in general. If not, even a USB stick might be a possibility, but it might not be elegant having something 'stick out of the device'. Don't forget these have different speeds, too. Some good webshops provide the speeds in their inventory list.

SSD is said to be slow on many small files. There are also now faster SSD with SATA2 support. As you can see from the list hereunder SSD doesn't have to be very expensive.

http://tweakers.net/pricewatch/cat/674 (I have a PATA Transcend)

http://tweakers.net/pricewatch/cat/48 (tons of several options)

Debian is good, especially as default OS, but one might prefer a different OS.

EDIT: I would swear I saw embedded devices with DVI (e.g. on picco.nl), but x86 (VIA for sure (Jetway mainbords), and perhaps AMD Geode). Not any RISC-based platform.