On one hand, the best way might be to propose the methods that led you to graduate and that you know firsthand worked primarily for you. After exploring the landscape of methods, you would then have to buy and explore them; you could start with these:
CURCI Fundamental Violin Technique, vol. I
LAOUREUX, Violin Method, vol. I
CRICKBOOM Le violon, Schott
The Dorflein Method, Schott
KALLAY, Violinschule, EMB
In particular for children, you could also use the following, which are nicely progressive:
CORINI My friend violin - Sinfonica
NELSON Complete Violin Method - Boosey & Hawkes
ALOIGI HAYES Alighiero and Miranda play together (Duets for open strings) - Boosey & Hawkes
CURCI Fundamental Violin Technique - Curci
but also
AZZARIO Bepi The musical marmot - Bmg
SASSMANNSHAUS Let's start early with the violin - Curci
PACE At school with the violin - Sinfonica
ALOIGI HAYES Alighiero plays scales - Boosey & Hawkes
I wouldn't let them miss out on something in duet, even with piano accompaniment:
Duets (two violins or violin and piano)
Early Music Fiddler Boosey
Ceilidh Collection Boosey
Klezmer Fiddler Boosey
Since we have done 30, let's make it 31....and the studies?
CURCI 24 Studies
SITT, 100 Studies op. 32, vol. I
WOLFHART Studies Op. 4 vol. I
SCHININA' Scales and arpeggios, vol. 1
SEVCIK op. 6
Buy everything, study them first...and choose