I only play 1 game online and it is WGT golf. We voice chat on Discord while we play. Would a INTEL 6300 DUAL CORE CPU processor be good enough to do this without game issues such as meter jumping?
Considering the minimum system requirements for the game is a 2GHz Pentium 4 (that was released 18ish years ago) a 6300 should be fine. However, if you are looking at a newer system going with something like a Ryzen 3 2200G or Ryzen 5 2400G would get you more bang for your buck in the long run.
To piggyback on the first post one of those ryzen cpu would work great for years and cost very little. Perhaps the best all around cpu that can do minor gaming. It's even strong enough to push a video card if you decide to play more intense games at some point.