If you haven't one already, then you need to find a suitable 78rpm stylus or styli set. If you want to work on the cheap then I would hunt for an appropriately priced Shure M78S 78-rpm moving magnet cartridge with stylus. Make sure you browse eBay and other online web sites as the price seems to vary as much as $80AUS!! The cheapest I have seen is around $35AUS on occasion for a new cartridge. Note that the Shure M78S is a 2.5-2.8mil non-truncated spherical stylus. The cartridge also comes with a wire link between the L and R output pins - remove this and record in stereo for best results.
Otherwise I recommend trying to get your hands on a re-tipped set of Stanton cartridges/styli or a Grado series. There may be others but you will have to shop around. Avoid ceramic and moving-coil cartridges altogether. Ceramic cartridges exhibit poor frequency characteristics that may interfere with the restoration process. Aged cartridges should also be avoided - crystal properties change and the rubber cantilever mount will have hardened with time affecting the sound.
The next important component is a good flat pre-amplifier. Several years back Rod Elliot published an article for a Multi Standard 78 RPM and RIAA Phono Equaliser. There are several circuits floating around on the web for such phono-pre amps but this one has the added benefit of multiple filter/turnover frequencies that can be used for normal listening or turned off when transcribing for later noise reduction. If you lack the ability to build such a circuit then you can still get away with using a normal RIAA equalised phono-pre amp. However, I would highly recommend you call in a friend who can!
Turntables themselves can pose a problem for some. If you are electronically minded and safety conscious when it comes to AC appliances, then you will have little issue in purchasing a nice 1980s DC-Servo controlled Direct Drive unit (or belt driven) and modifying the electronic feedback mechanism to allow the platter to rotate at 78rpm. Direct drive is always better as there is no belt to wear out and this will likely occur at a faster rate post-modification. A couple of good blog's cover the process with different approaches and can be readily applied to similar units of other makes:
If you find any thought of DC electronics challenging then I would recommend getting an electronically minded friend to do the work as the results are definitely worth the effort. However, if this is beyond you then you will just have to make recordings at 45rpm and digitally modify the speed later. This doesn't pose a problem, each recording just takes that little bit longer to transcribe!