Oh dear, I'm going to disagree with m'learned colleagues.
Even if you own a grinding wheel, one of the skills a learner will find difficult at the outset is grinding HSS toolbits. Therefore, I'd suggest that most learners will be better off starting buying a ready made set, such as this one, which has a useful range of shapes that aren't made of putty.
I've never got on well with brazed carbide tipped tools, but indexable are a much better bet. Again, for a beginner with a fast modern lathe, indexable tips solve an absent skills problem. Another advantage If you break a tip is that they are easily changed without disturbing the set-up. Provided you own a fast lathe the main objections to indexable tools are cost and getting the best possible finish in hobby use. I didn't buy a set; I bought a right-hand and a left-hand holder and a small-boring bar. They kept me happy for a year.
Once you've got a feel for what your new lathe can do, then it's time to experiment with hand ground HSS. Don't get me wrong, it's well worth learning how to shape and sharpen HSS: all I'm suggesting is don't make 'not knowing how to' a show-stopper on day one!
Dave
Edit punctuation
Edited By SillyOldDuffer on 01/05/2017 10:47:51