It's a bit of a bugbear of mine, as someone who teaches anglo, that many of the tutor books out there are so focussed on one style of playing that they don't explain the alternatives to a beginner.

There are essentially two anglo styles that are popular today in traditional music: (1) Playing the melody across both ends of the instrument, as against (2) playing the melody mostly on the right hand, in order to leave the left hand free for harmonic accompaniment.

The former is best-known in Irish traditional music, which is also characterised by a lot of ornamentation. Think Mary MacNamara or Noel Hill. Harmonic style is what mostly English musicians from William Kimber to John Kirkpatrick play.

The thing is, it's very difficult to combine the two styles (Benedict Gagliardi of the Voxhunters has taken the Irish style and added a lot more chording than is usual - but then, he's a virtuoso). Some Irish players do add chords, but much more sporadically than a player like John K. would.

So, as a player new to the instrument, you have to make a choice straight away: single-note melody, or harmonized. If you go down the single-note track, it's very difficult to convert to harmony later, because your LH fingers are too busy playing the tune to add chords.

The other complication is that the most common key for the anglo is C/G. A good Irish-style player using basically single-note style would be able to play that instrument in a variety of keys including D and A, i.e. the kinds of keys that fiddlers prefer. If you want to play harmonic style, however, it's much more difficult to switch into keys outside the home ones without losing the LH harmony. This is why some players of harmonic style get themselves a G/D so they can play along in a session (also it sound less trebly).

So you really do have to make a decision. If you really like the 'one man band' sound of a fully harmonized style, and you own a C/G, then it will be harder to take it to the session and join in. If you decide on single-note melody, then you will be free to explore the subtle delights of the Irish style, but don't come to me afterwards saying you want to play morris dance tunes like John K. does!