1) What gauge of strings are you using now? Do you remember what strings were on the guitar, which you replaced now?
2) Alpha1 said - Little buzz on thicker strings is common on the first few frets, I Disagree, ideally there should be no buzz anywhere, unless and until the fretting is not right.....
3) Truss rod adjustment should not be the ultimate way to deal with buzz, the first thing to check is if the neck has a bow, forward or backward bow....that tells how the neck is behaving to the new strings.....
4) If there is some bow, thats when the truss adj should be carried out, that too with extreme care, you may break the truss rod or damage the neck permanently.
5) I would suggest, loosen the strings, so you can pull the Bridge Saddle out, place a thin piece of paper underneath where the bridge saddle sits, ensure its fit snug and does not cover the sides of the saddle slot. this will increase the height just a little when the bridge sits on the paper. Place the bridge on the paper, tighten the strings, tune the guitar and check if any difference can be heard/seen.
6) Also check the nut at the neck, if the slots are too deep, it can cause the strings to buzz, ensure that the string sits just on top of the nut with some part of the string exposed out of the nut slot......it is really critical that the string is not buried into the nut slot, this may cause your guitar to go out of tune very often....Use a pencil tip, and rub it on top of the nut if you find the nut slots fine, this will allow the string to move around the slot freely and will hold on to its tuning better than before.....
If all this fails, take it to a luthier who can fix it for you........a buzzing guitar is never good.
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