The best suture material I have found that anyone can purchase online is the brand Unify, available through Amazon and elsewhere. For suturing of skin wounds, the 3-0 and 4-0 Nylon are most useful to have on hand, though having some 5-0 available for lacerations of tender skin (face/children/fingers) is a good idea.
For my own patients, I use professional suture, which does cost more, but is more difficult for the layman to procure. (Check back soon – I may begin offering this for sale on my own site.)
The only problems I have had with the Unify suture, which I use for my live Survival Medicine classes, is that the needles may bend a little easier and the suture may detach from the needle a little easier than higher grade suture. Still, I believe they are adequate for most wound closure and anyone can get them.