the speed of your turntable is correct. Use
a strobe disc and a fluorescent or neon lamp operating off of your AC line for
this purpose, provided that you live in an area where the power line frequency
is accurate and stable. If the
speed is incorrect, use the turntable pitch control to correct the anomaly.
Note whether or not the record groove is rotating concentrically. If it is not, there will be a "Wow" effect on the recording. This problem can be corrected if your turntable has a removable spindle. With the spindle removed, adjust the position of the record with respect to the turntable platter until the stylus tracks the record concentrically.
45 and 33 1/3 LPs are pretty standard though 78 speeds can vary.
Most Victor, Columbia , and other 78's were actually recorded at 78.26 RPM, however, Edison laterals were recorded at 78.8 RPM. Edison Diamond Discs were recorded at 80 RPM.
Just make sure you match the speed to the requirements of your record.