Hi Brian,
There are a couple of us into 78s here in the GAS Circle, namely me and Blackmore.
When it comes to 78s, it's not just a matter of the platter spinning faster but you also have a different stylus profile and 78s have scads of different equalization curves. Post 1955(ish) the industry standardized on the RIAA curve which is still followed today.
Here is a quick link to most all of the different curves used by the various recording companies over the years.
http://www.shellac.org/wams/wequal.htmlI'm not trying to scare you off by any stretch. If you get a 78 player and appropriate cartridge and stylus, music will absolutely come out of the other end of the system. It just may not sound as great as it could when you apply the right equalization.
You can accomplish the proper equalization a few different ways. One, you could buy a dedicated 78 phonostage. There are several out there. Graham Slee and several others offer them though they can get really pricey, really quick. I have the Slee and it works quite well. But that isn't how I play mine back. I have a dedicated mono system just for 78s and it isn't overly expensive to put together.

What this is, is an old Stromberg Carlson SC420 amp (cira 1954ish), an old Altec 824 speaker and an old Dual 1210 with a Shure M78 cart and stylus.
Here is a closer look at the Stromberg (this is my spare amp). You can see that the Stromberg has a variable equalization curve that covers everything recorded prior to 1955.
This little system is serious fun. Forget about fidelity, though there are times on the right recording magic comes out of the speaker, this is just plain fun to listen to. It doesn't matter if its old blues, western, jazz or the pop stars of the day, its thoroughly pleasurable to listen to....4 minutes at a time. That system wouldn't cost more than $500 or so to assemble.
So, that would be my suggestion. Build a dedicated system. It doesn't cost much at all (in comparison) and doesn't take up much room either. No worries about speaker placement, expensive cables, soundstage or any of the 'audiophile' obsessions. It just plays
music.
Good luck