"The Mini Lathe" by David Fenner is a nice little book for the beginner, with good information about cutters and tools. It costs about 10 dollars including S&H at The Book Depository. You can also find free e-books about lathework at the Open Library, they were published in the 19th century but much of the information is quite valuable. I've found a few free books on model engineering at the same place. Those old books describe the work model engineers had to do with lathes without electric motors and with very basic tooling.
For my first engine, a small 7 mm oscillator I used: 7mm, 1.2mm, 2.5mm, 3mm drill bits, right hand cutter, M3 tap. For me, part of the fun with every project is on the trips I have to do to the hardware store, just keep your expenses on check.