If you have the freedom of choice, I'd go for phil's super socket 7 build - it looks like a very neat way of handling multiple games.
I've gone for a pentium ii 300MHz, mostly because it's almost silent - the only fan is in the PSU. Other factors were the fact it was donated to me, faster than the (noisy) Cyrix MII 300 system I used previously, and well built.
The rationale is :
2 ISA slots (one shared PCI/ISA).
Fast enough to run practically all DOS games
S3 Savage 4 - compatible with most DOS games
AWE64 - sound, MIDI interface for external modules
NIC for LAN connectivity
Voodoo 2
The motherboard has an AGP slot, but most of the AGP cards are not as compatible with DOS games, especially stuff like Commander Keen.
The Voodoo2 isn't actually very useful. It's needed to run the first Tomb Raider in its original state, and Screamer. Practically everything else works fine on a modern system with a 3D card, there's a high resolution mod to the first Tomb Raider, and that requires a glide emulator and a modern card.
Likewise, Duke Nukem runs really well in high resolution, but I'm not sure if it's worth the bother given the excellent eDuke32. Sound Canvas support might be an advantage, maybe.
It's too fast to run Sam and Max properly, with external MIDI, and probably too fast for the Ultima series too. So, I'm going to use a 486 for that - and yes, they're a pain in the arse.
I do have a few toys for it - an hxc floppy emulator, which is excellent, and a semi enterprise SSD (80GB Intel, DC3500) linked to an IDE to SATA converter. 80GB is way more than I need, and cost wise there weren't any half decent SSDs any cheaper at the time. Using both of those makes the system extremely quiet.