My own installation was with Debian 1.3.1 but Red Hat, Slackware and others should work fine too. The main recommendation I would make in choosing a Linux distribution, is to ensure that the version of XFree86 supports the Compaq AVGA video chip.
The following distributions have been reported to install and operate with success:
If you have the expansion base, then there are several installation methods, the most straightforward being to fit a CDROM to the expansion base and install Linux from there. The method that I have used and recommend is to install an ethernet card to the expansion base and install Linux using nfs or ftp.
If you don't have the expansion base, then installation can be a little more difficult. You may find that some installations allow you to boot from the boot disk and install via slip or ppp. Otherwise you can install a basic system from floppy or DOS partition, then get networking/ppp running to complete the installation.
Please note: There have been reports of not being able to access an IDE CDROM when installed in the expansion base. I have not had an opportunity to test this. If this method doesn't work for you, I can only suggest you try one of the other methods to install Linux.
I am now recommending that you don't rely on any IDE device working with Linux in the expansion base. It seems that this would make an IDE/ATAPI CDROM installation difficult to achieve, unless an IDE interface card could be installed in one of the ISA slots. I intend to add an installation problems section or sub-section to this document, which may cover this in more detail.