Doesn't look like emulators can do EAX, PCEM goes as far as AWE32 or PCI128.
If you mix 98 and XP, then the 98 is going to determine the maximum you can go to, basically the end of AGP.
Also, EAX means a PCI (or maybe PCIE in XP) sound card, and PCI sound is not DOS friendly - there are some combinations that work but they depend on certain features

There are some s478 and very few lga775 boards that have full ISA support.

You can also look at doing one of the lpc to isa slot conversions on a much newer board.

The DOSBox variants should cover 99% of pre-Win95 titles. Or you could emulate an entire machine using any of the popular VM solutions. Just be aware that there will always be some games that rely on something unsupported or trigger a bug and that you'll have to do without. But then again a single physical build wouldn't get you to 100% support either. There's always a tradeoff.

PCEM has a stated upper limit for its emulation target (I forget what exactly, something around a Pentium 2 or 3 with a Voodoo 2 or 3 I think). Not entirely sure about EAX - I think PCEM's target is a bit before EAX became relevant iirc. But it will get you well into Win9x territory at least. Other generic VM solutions will probably lack support to emulate specific cards if a game is a bit picky, but they can still be worth a try since they do not self-impose any limits. There's a QEMU mod with 3Dfx support (...passthrough? emulation? I forget) that might come in handy.

XP is in a bit of a bad spot, emulation-wise. GPU acceleration in VMs can be hit or miss, and the support for specific audio features is looking pretty poor also. If you can deal with keeping an extra physical machine aside from your main one, this is what I would blow that budget on. A notebook might work if you can do without EAX altogether (or were there models with this feature? Don't recall seeing any), but I'd strongly recommend making a compromise and going for/sticking with a regular PC. It doesn't need to take up a lot of space, small form factor cases do exist [edit: d'oh - just noticed you're already using one]. You can put an X-Fi card in there for EAX, and also use it for some Win9x era games. You might've read that GPU compatibility (backwards compatibility with older DirectX versions) can be problematic; this is true, but it'll be much less of an issue if you'll be running earlier titles elsewhere (emulated on your main) anyways.

Most titles from late XP onwards (rule of thumb - those targeting Vista but still supporting XP as a "legacy OS") you should be able to get to work natively, using some patches where necessary, and not too many wrappers. But I'll say it again, without a reasonable collection of actual vintage hardware you won't be able to cover all 100%, "only" the vast majority.

TL;DR: For DOS/Win16: DOSBox on your main PC; Win9x: PCEM on your main PC; WinXP/EAX: dedicated box; Vista and up: natively on your main PC.