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I recently ran into the same problem when I found my old Myst CD.
I've found solutions to most of my old games with Dosbox and ScummVM but the Windows 95/98 games are a bit trickier.
It takes quite a bit of setting up (it took me far longer than I'd care to admit) but a Virtual Machine running Windows XP works a treat.
Not too difficult, just a little fiddly. If you find a good guide online, (provided you have access the required software) you shouldn't have a problem.
Once set up, a VM allows you to install and play the game exactly as it was intended, fantastic for those games stuck in limbo between working on an emulator and working on modern systems.
So for single player I just use my native install with the draw.dll patch which works ok, but for battle.net (which is a bit quiet to be honest) I just boot up XP in the virtual machine and it's like stepping back in time.
Edit: Make sure to patch up to 1.9 or Battle.net wont find any servers.