According to the literatures, I noticed some of researchers used buffer solution for the preparation of heavy metal ions, whereas the others are not and they just used deionized water for the preparation and dilution process. Which one is correct?
I think you should give more details of the question background (which elements; purpose of approach). When you prepare metal solution for analytical standards the addition of a buffer is not a good idea because you add matrix elements of possibly unknown purity. Dealing with high matrix solutions (e.g. high salt load) standard addition would be ok. Heavy metals in neutral deonized water tend to hydrolyse, i.e. they will precipitate. The effect depends on the element, the concentration, and the aging time. Using acid solutions the precipitation can be prevented. To be on the save side a molarity of 0.1N to 1N should do (e.g. 1N HNO3; but there are exceptions); you have to try out.
When dealing with adsorption isotherms a background solution will be necessary; but I would not like to define this as a buffer.
One reason for adding buffers is that some "heavy metal" ions tend to hydrolyze and form not only precipitates, but e.g. hydroxo complexes, so they don't exist in aqueous solutions just as solvated ions. Sn2+ is typical in this respect. This discussion can go on and on, but pH may be really critical in some situations.